Simple Harmonic Motion · Physics · JEE Main

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MCQ (Single Correct Answer)

1

A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is 200 N/m. The block is pushed such that the length of the spring becomes 1 m and then released. At distance x m (x < 2) from the wall, the speed of the block will be

JEE Main 2025 (Online) 8th April Evening Shift
2

Two simple pendulums having lengths $l_1$ and $l_2$ with negligible string mass undergo angular displacements $\theta_1$ and $\theta_2$, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?

JEE Main 2025 (Online) 4th April Morning Shift
3
JEE Main 2025 (Online) 3rd April Morning Shift Physics - Simple Harmonic Motion Question 2 English

Two blocks of masses $m$ and $M,(M>m)$, are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released, then ( $\mu=$ coefficient of friction between the two blocks)

A. The time period of small oscillation of the two blocks is $T=2 \pi \sqrt{\frac{(m+M)}{k}}$

B. The acceleration of the blocks is $a=-\frac{k x}{M+m}$ ( $x=$ displacement of the blocks from the mean position)

C. The magnitude of the frictional force on the upper block is $\frac{m \mu|x|}{M+m}$

D. The maximum amplitude of the upper block, if it does not slip, is $\frac{\mu(M+m) g}{k}$

E. Maximum frictional force can be $\mu(\mathrm{M}+\mathrm{m}) \mathrm{g}$.

Choose the correct answer from the options given below :

JEE Main 2025 (Online) 3rd April Morning Shift
4

A particle is subjected to two simple harmonic motions as : $$ x_1=\sqrt{7} \sin 5 \mathrm{tcm} $$ and $x_2=2 \sqrt{7} \sin \left(5 t+\frac{\pi}{3}\right) \mathrm{cm}$ where $x$ is displacement and $t$ is time in seconds. The maximum acceleration of the particle is $x \times 10^{-2} \mathrm{~ms}^{-2}$. The value of $x$ is :

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5

Two bodies A and B of equal mass are suspended from two massless springs of spring constant k1 and k2, respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the maximum velocity of B is

JEE Main 2025 (Online) 29th January Evening Shift
6

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain.

Reason (R) : Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa.

In the light of the above statements, choose the most appropriate answer from the options given below :

JEE Main 2025 (Online) 29th January Morning Shift
7

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : Knowing initial position $\mathrm{x}_0$ and initial momentum $p_0$ is enough to determine the position and momentum at any time $t$ for a simple harmonic motion with a given angular frequency $\omega$.

Reason (R) : The amplitude and phase can be expressed in terms of $\mathrm{X}_0$ an $\mathrm{p}_0$.

In the light of the above statements, choose the correct answer from the options given below :

JEE Main 2025 (Online) 28th January Evening Shift
8

A particle oscillates along the $x$-axis according to the law, $x(\mathrm{t})=x_0 \sin ^2\left(\frac{\mathrm{t}}{2}\right)$ where $x_0=1 \mathrm{~m}$. The kinetic energy $(\mathrm{K})$ of the particle as a function of $x$ is correctly represented by the graph

JEE Main 2025 (Online) 24th January Evening Shift
9
A particle is executing simple harmonic motion with time period 2 s and amplitude 1 cm . If D and d are the total distance and displacement covered by the particle in 12.5 s , then $\frac{\mathrm{D}}{\mathrm{d}}$ is
JEE Main 2025 (Online) 24th January Morning Shift
10

A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is $y \pi \times 10^{-2} \mathrm{~s}$, where the value of $y$ is (Acceleration due to gravity, $g=10 \mathrm{~m} / \mathrm{s}^2$, density of water $=10^3 \mathrm{~kg} / \mathrm{m}^3$ )

JEE Main 2025 (Online) 23rd January Morning Shift
11

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet.

Reason (R) : The mass of the pendulum remains unchanged at Earth and the other planet.

In the light of the above statements, choose the correct answer from the options given below :

JEE Main 2025 (Online) 22nd January Evening Shift
12

A simple pendulum doing small oscillations at a place $$R$$ height above earth surface has time period of $$T_1=4 \mathrm{~s}$$. $$\mathrm{T}_2$$ would be it's time period if it is brought to a point which is at a height $$2 \mathrm{R}$$ from earth surface. Choose the correct relation [$$\mathrm{R}=$$ radius of earth] :

JEE Main 2024 (Online) 5th April Morning Shift
13

In simple harmonic motion, the total mechanical energy of given system is $$E$$. If mass of oscillating particle $$P$$ is doubled then the new energy of the system for same amplitude is:

JEE Main 2024 (Online) 4th April Evening Shift Physics - Simple Harmonic Motion Question 15 English

JEE Main 2024 (Online) 4th April Evening Shift
14
A simple pendulum of length $1 \mathrm{~m}$ has a wooden bob of mass $1 \mathrm{~kg}$. It is struck by a bullet of mass $10^{-2} \mathrm{~kg}$ moving with a speed of $2 \times 10^2 \mathrm{~ms}^{-1}$. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is. (use $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )
JEE Main 2024 (Online) 1st February Morning Shift
15

The bob of a pendulum was released from a horizontal position. The length of the pendulum is $$10 \mathrm{~m}$$. If it dissipates $$10 \%$$ of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is:

[Use, $$\mathrm{g}: 10 \mathrm{~ms}^{-2}$$]

JEE Main 2024 (Online) 29th January Evening Shift
16
In a linear Simple Harmonic Motion (SHM)

(A) Restoring force is directly proportional to the displacement.

(B) The acceleration and displacement are opposite in direction.

(C) The velocity is maximum at mean position.

(D) The acceleration is minimum at extreme points.

Choose the correct answer from the options given below:
JEE Main 2023 (Online) 15th April Morning Shift
17

A particle executes SHM of amplitude A. The distance from the mean position when its's kinetic energy becomes equal to its potential energy is :

JEE Main 2023 (Online) 13th April Evening Shift
18

Which graph represents the difference between total energy and potential energy of a particle executing SHM vs it's distance from mean position ?

JEE Main 2023 (Online) 13th April Morning Shift
19

A particle is executing simple harmonic motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be

JEE Main 2023 (Online) 12th April Morning Shift
20

The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement $$(x)$$ starting from mean position to extreme position (A) is given by

JEE Main 2023 (Online) 11th April Morning Shift
21

A particle executes S.H.M. of amplitude A along x-axis. At t = 0, the position of the particle is $$x=\frac{A}{2}$$ and it moves along positive x-axis. The displacement of particle in time t is $$x = A\sin (wt + \delta )$$, then the value of $$\delta$$ will be

JEE Main 2023 (Online) 10th April Morning Shift
22

For particle P revolving round the centre O with radius of circular path $$\mathrm{r}$$ and angular velocity $$\omega$$, as shown in below figure, the projection of OP on the $$x$$-axis at time $$t$$ is

JEE Main 2023 (Online) 8th April Evening Shift Physics - Simple Harmonic Motion Question 29 English

JEE Main 2023 (Online) 8th April Evening Shift
23

A mass $$m$$ is attached to two strings as shown in figure. The spring constants of two springs are $$\mathrm{K}_{1}$$ and $$\mathrm{K}_{2}$$. For the frictionless surface, the time period of oscillation of mass $$m$$ is :

JEE Main 2023 (Online) 6th April Morning Shift Physics - Simple Harmonic Motion Question 28 English

JEE Main 2023 (Online) 6th April Morning Shift
24

Choose the correct length (L) versus square of the time period ($$\mathrm{T}^{2}$$) graph for a simple pendulum executing simple harmonic motion.

JEE Main 2023 (Online) 1st February Evening Shift
25

The maximum potential energy of a block executing simple harmonic motion is $$25 \mathrm{~J}$$. A is amplitude of oscillation. At $$\mathrm{A / 2}$$, the kinetic energy of the block is

JEE Main 2023 (Online) 31st January Morning Shift
26

For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is $1 \mathrm{~kg}$, the angular frequency is $\omega_{1}$. When the mass block is $2 \mathrm{~kg}$ the angular frequency is $\omega_{2}$. The ratio $\omega_{2} / \omega_{1}$ is

JEE Main 2023 (Online) 30th January Evening Shift Physics - Simple Harmonic Motion Question 45 English

JEE Main 2023 (Online) 30th January Evening Shift
27

A particle executes simple harmonic motion between $$x=-A$$ and $$x=+A$$. If time taken by particle to go from $$x=0$$ to $$\frac{A}{2}$$ is 2 s; then time taken by particle in going from $$x=\frac{A}{2}$$ to A is

JEE Main 2023 (Online) 25th January Evening Shift
28

T is the time period of simple pendulum on the earth's surface. Its time period becomes $$x$$ T when taken to a height R (equal to earth's radius) above the earth's surface. Then, the value of $$x$$ will be :

JEE Main 2023 (Online) 25th January Morning Shift
29

The time period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination $$\alpha$$, is given by :

JEE Main 2022 (Online) 29th July Morning Shift
30

Assume there are two identical simple pendulum clocks. Clock - 1 is placed on the earth and Clock - 2 is placed on a space station located at a height h above the earth surface. Clock - 1 and Clock - 2 operate at time periods 4 s and 6 s respectively. Then the value of h is -

(consider radius of earth $$R_{E}=6400 \mathrm{~km}$$ and $$\mathrm{g}$$ on earth $$10 \mathrm{~m} / \mathrm{s}^{2}$$ )

JEE Main 2022 (Online) 28th July Evening Shift
31

When a particle executes Simple Hormonic Motion, the nature of graph of velocity as a function of displacement will be :

JEE Main 2022 (Online) 26th July Morning Shift
32

JEE Main 2022 (Online) 25th July Morning Shift Physics - Simple Harmonic Motion Question 57 English

In figure $$(\mathrm{A})$$, mass '$$2 \mathrm{~m}^{\text {' }}$$ is fixed on mass '$$\mathrm{m}$$ ' which is attached to two springs of spring constant $$\mathrm{k}$$. In figure (B), mass '$$\mathrm{m}$$' is attached to two springs of spring constant '$$\mathrm{k}$$' and '$$2 \mathrm{k}^{\prime}$$. If mass '$$\mathrm{m}$$' in (A) and in (B) are displaced by distance '$$x^{\prime}$$ horizontally and then released, then time period $$\mathrm{T}_{1}$$ and $$\mathrm{T}_{2}$$ corresponding to $$(\mathrm{A})$$ and (B) respectively follow the relation.

JEE Main 2022 (Online) 25th July Morning Shift
33

The motion of a simple pendulum executing S.H.M. is represented by the following equation.

$$y = A\sin (\pi t + \phi )$$, where time is measured in second. The length of pendulum is

JEE Main 2022 (Online) 29th June Evening Shift
34

Motion of a particle in x-y plane is described by a set of following equations $$x = 4\sin \left( {{\pi \over 2} - \omega t} \right)\,m$$ and $$y = 4\sin (\omega t)\,m$$. The path of the particle will be :

JEE Main 2022 (Online) 28th June Morning Shift
35

The equation of a particle executing simple harmonic motion is given by $$x = \sin \pi \left( {t + {1 \over 3}} \right)m$$. At t = 1s, the speed of particle will be

(Given : $$\pi$$ = 3.14)

JEE Main 2022 (Online) 27th June Evening Shift
36

The displacement of simple harmonic oscillator after 3 seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is :

JEE Main 2022 (Online) 27th June Morning Shift
37

Time period of a simple pendulum in a stationary lift is 'T'. If the lift accelerates with $${g \over 6}$$ vertically upwards then the time period will be :

(Where g = acceleration due to gravity)

JEE Main 2022 (Online) 26th June Morning Shift
38

Two massless springs with spring constants 2 k and 9 k, carry 50 g and 100 g masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be :

JEE Main 2022 (Online) 24th June Evening Shift
39
A mass of 5 kg is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length 4 m has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed?

JEE Main 2021 (Online) 1st September Evening Shift Physics - Simple Harmonic Motion Question 67 English
JEE Main 2021 (Online) 1st September Evening Shift
40
A bob of mass 'm' suspended by a thread of length l undergoes simple harmonic oscillations with time period T. If the bob is immersed in a liquid that has density $${1 \over 4}$$ times that of the bob and the length of the thread is increased by 1/3rd of the original length, then the time period of the simple harmonic oscillations will be :-
JEE Main 2021 (Online) 31st August Evening Shift
41
For a body executing S.H.M. :

(1) Potential energy is always equal to its K.E.

(2) Average potential and kinetic energy over any given time interval are always equal.

(3) Sum of the kinetic and potential energy at any point of time is constant.

(4) Average K.E. in one time period is equal to average potential energy in one time period.

Choose the most appropriate option from the options given below :
JEE Main 2021 (Online) 31st August Evening Shift
42
The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure.

JEE Main 2021 (Online) 27th August Morning Shift Physics - Simple Harmonic Motion Question 72 English
The potential energy U(x) versus time (t) plot of the particle is correctly shown in figure :
JEE Main 2021 (Online) 27th August Morning Shift
43
An object of mass 0.5 kg is executing simple harmonic motion. It amplitude is 5 cm and time period (T) is 0.2 s. What will be the potential energy of the object at an instant $$t = {T \over 4}s$$ starting from mean position. Assume that the initial phase of the oscillation is zero.
JEE Main 2021 (Online) 27th July Evening Shift
44
A particle starts executing simple harmonic motion (SHM) of amplitude 'a' and total energy E. At any instant, its kinetic energy is $${{3E} \over 4}$$ then its displacement 'y' is given by :
JEE Main 2021 (Online) 27th July Morning Shift
45
In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.
JEE Main 2021 (Online) 25th July Evening Shift
46
T0 is the time period of a simple pendulum at a place. if the length of the pendulum is reduced to $${1 \over {16}}$$ times of its initial value, the modified time period is :
JEE Main 2021 (Online) 22th July Evening Shift
47
A particle is making simple harmonic motion along the X-axis. If at a distances x1 and x2 from the mean position the velocities of the particle are v1 and v2 respectively. The time period of its oscillation is given as :
JEE Main 2021 (Online) 20th July Evening Shift
48
The function of time representing a simple harmonic motion with a period of $${\pi \over \omega }$$ is :
JEE Main 2021 (Online) 18th March Evening Shift
49
The time period of a simple pendulum is given by $$T = 2\pi \sqrt {{l \over g}} $$. The measured value of the length of pendulum is 10 cm known to a 1mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 second using a clock of 1s resolution. The percentage accuracy in the determination of 'g' using this pendulum is 'x'. The value of 'x' to be nearest integer is :-
JEE Main 2021 (Online) 18th March Morning Shift
50
Two particles A and B of equal masses are suspended from two massless springs of spring constants K1 and K2 respectively. If the maximum velocities during oscillations are equal, the ratio of the amplitude of A and B is
JEE Main 2021 (Online) 17th March Evening Shift
51
A block of mass 1 kg attached to a spring is made to oscillate with an initial amplitude of 12 cm. After 2 minutes the amplitude decreases to 6 cm. Determine the value of the damping constant for this motion . (take ln 2 = 0.693)
JEE Main 2021 (Online) 17th March Evening Shift
52
For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal ?
JEE Main 2021 (Online) 17th March Morning Shift
53
Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass = 500g, Decay constant = 20 g/s then how much time is required for the amplitude of the system to drop to drop to half of its initial value? (ln 2 = 0.693)
JEE Main 2021 (Online) 16th March Evening Shift
54
Time period of a simple pendulum is T inside a lift when the lift is stationary. If the lift moves upwards with an acceleration g/2, the time period of pendulum will be :
JEE Main 2021 (Online) 16th March Morning Shift
55
A particle executes S.H.M., the graph of velocity as a function of displacement is :
JEE Main 2021 (Online) 26th February Evening Shift
56
Given below are two statements :

Statement I : A second's pendulum has a time period of 1 second.

Statement II : It takes precisely one second to move between the two extreme positions.

In the light of the above statements, choose the correct answer from the options given below :
JEE Main 2021 (Online) 26th February Evening Shift
57
Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance (R/2) from the earth's centre, where 'R' is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period :
JEE Main 2021 (Online) 26th February Morning Shift
58
If two similar springs each of spring constant K1 are joined in series, the new spring constant and time period would be changed by a factor :
JEE Main 2021 (Online) 26th February Morning Shift
59
Y = A sin($$\omega$$t + $$\phi$$0) is the time-displacement equation of a SHM. At t = 0 the displacement of the particle is $$Y = {A \over 2}$$ and it is moving along negative x-direction. Then the initial phase angle $$\phi$$0 will be:
JEE Main 2021 (Online) 25th February Evening Shift
60
Two identical springs of spring constant '2k' are attached to a block of mass m and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this system is :

JEE Main 2021 (Online) 25th February Evening Shift Physics - Simple Harmonic Motion Question 99 English
JEE Main 2021 (Online) 25th February Evening Shift
61
The point A moves with a uniform speed along the circumference of a circle of radius 0.36 m and covers 30$$^\circ$$ in 0.1 s. The perpendicular projection 'P' from 'A' on the diameter MN represents the simple harmonic motion of 'P'. The restoration force per unit mass when P touches M will be :

JEE Main 2021 (Online) 25th February Evening Shift Physics - Simple Harmonic Motion Question 98 English
JEE Main 2021 (Online) 25th February Evening Shift
62
If the time period of a two meter long simple pendulum is 2s, the acceleration due to gravity at the place where pendulum is executing S.H.M. is :
JEE Main 2021 (Online) 25th February Morning Shift
63
In the given figure, a body of mass M is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant k, the frequency of oscillation of given body is :

JEE Main 2021 (Online) 24th February Evening Shift Physics - Simple Harmonic Motion Question 103 English
JEE Main 2021 (Online) 24th February Evening Shift
64
When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is :
JEE Main 2021 (Online) 24th February Evening Shift
65
The period of oscillation of a simple pendulum is $$T = 2\pi \sqrt {{L \over g}} $$. Measured value of 'L' is 1.0 m from meter scale having a minimum division of 1 mm and time of one complete oscillation is 1.95 s measured from stopwatch of 0.01 s resolution. The percentage error in the determination of 'g' will be :
JEE Main 2021 (Online) 24th February Evening Shift
66
In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k. The mass oscillates on a frictionless surface with time period T and amplitude A. When the mass is in equilibrium position, as shown in the figure, another mass m is gently fixed upon it. The new amplitude of oscillations will be :

JEE Main 2021 (Online) 24th February Morning Shift Physics - Simple Harmonic Motion Question 104 English
JEE Main 2021 (Online) 24th February Morning Shift
67
When a particle of mass m is attached to a vertical spring of spring constant k and released, its motion is described by
y(t) = y0 sin2 $$\omega $$t, where 'y' is measured from the lower end of unstretched spring. Then $$\omega $$ is:
JEE Main 2020 (Online) 6th September Evening Slot
68
A block of mass m attached to a massless spring is performing oscillatory motion of amplitude ‘A’ on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become fA. The value of f is :
JEE Main 2020 (Online) 3rd September Evening Slot
69
The displacement time graph of a particle executing S.H.M is given in figure :
(sketch is schematic and not to scale) JEE Main 2020 (Online) 2nd September Evening Slot Physics - Simple Harmonic Motion Question 107 English
Which of the following statements is/are true for this motion?
(A) The force is zero at t = $${{3T} \over 4}$$
(B) The acceleration is maximum at t = T
(C) The speed is maximum at t = $${{T} \over 4}$$
(D) The P.E. is equal to K.E. of the oscillation at t = $${{T} \over 2}$$
JEE Main 2020 (Online) 2nd September Evening Slot
70
A spring mass system (mass m, spring constant k and natural length $$l$$) rest in equilibrium on a horizontal disc. The free end of the spring is fixed at the centre of the disc. If the disc together with spring mass system, rotates about it's axis with an angular velocity $$\omega $$, (k $$ \gg m{\omega ^2}$$) the relative change in the length of the spring is best given by the option :
JEE Main 2020 (Online) 9th January Evening Slot
71
A simple pendulum is being used to determine th value of gravitational acceleration g at a certain place. Th length of the pendulum is 25.0 cm and a stop watch with 1s resolution measures the time taken for 40 oscillations to be 50 s. The accuracy in g is :
JEE Main 2020 (Online) 8th January Evening Slot
72
The displacement of a damped harmonic oscillator is given by
x(t ) = e–0.1t cos (10$$\pi $$t + f).
Here t is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value is close to :
JEE Main 2019 (Online) 10th April Morning Slot
73
A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations. The time it will take to drop to 1/1000 of the original amplitude is close to :-
JEE Main 2019 (Online) 8th April Evening Slot
74
A simple harmonic motion is represented by :

y = 5 (sin 3 $$\pi $$ t + $$\sqrt 3 $$ cos 3 $$\pi $$t) cm

The amplitude and time period of the motion are :
JEE Main 2019 (Online) 12th January Evening Slot
75
Two light identical springs of spring constant k are attached horizontally at the two ends of a uniform horizontal rod AB of length $$\ell $$ and mass m. The rod is pivoted at its centre 'O' and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is :

JEE Main 2019 (Online) 12th January Morning Slot Physics - Simple Harmonic Motion Question 113 English
JEE Main 2019 (Online) 12th January Morning Slot
76
The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of simple pendulum on the Earth is 2 s. The period of oscillation of the same pendulum on the planet would be :
JEE Main 2019 (Online) 11th January Evening Slot
77
A pendulum is executing simple harmonic motion and its maximum kinetic energy is K1. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is K2. Then :
JEE Main 2019 (Online) 11th January Evening Slot
78
A simple pendulum of length 1 m is oscillating with an angular frequency 10 rad/s. The support of the pendulum starts oscillating up and down with a small angular frequency of 1 rad/s and an amplitude of 10–2 m. The relative change in the angular frequency of the pendulum is best given by :
JEE Main 2019 (Online) 11th January Evening Slot
79
A particle undergoing simple harmonic motion has time dependent displacement given by x(t) = Asin$${{\pi t} \over {90}}$$. The ratio of kinetic to potential energy of this particle at t = 210 s will be:
JEE Main 2019 (Online) 11th January Morning Slot
80
A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in seconds is -
JEE Main 2019 (Online) 10th January Evening Slot
81
A cylindrical plastic bottle of negligible mass is filled with 310 ml of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency $$\omega $$. If the radius of the bottle is 2.5 cm then $$\omega $$ is close to – (density of water = 103 kg/m3).
JEE Main 2019 (Online) 10th January Evening Slot
82
A closed organ pipe has a fundamental frequency of 1.5 kHz. The number of overtones that can be distinctly heard by a person with this organ pipe will be (Assume that the highest frequency a person can hear is 20,000 Hz)
JEE Main 2019 (Online) 10th January Evening Slot
83
A rod of mass 'M' and length '2L' is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of 'm' are attached at distance 'L/2' from its centre on both sides, it reduces the oscillation frequency by 20%. The value of radio m/M is close to :
JEE Main 2019 (Online) 9th January Evening Slot
84
A particle is executing simple harmonic motion (SHM) of amplitude A, along the x-axis, about x = 0. When its potential Energy (PE) equals kinetic energy (KE), the position of the particle will be :
JEE Main 2019 (Online) 9th January Evening Slot
85
An oscillator of mass M is at rest in its equilibrium position in a potential
V = $${1 \over 2}$$ k(x $$-$$ X)2. A particle of mass m comes from right with speed u and collides completely inelastically with M and sticks to it. This process repeats every time the oscillator crosses its equilibrium position. The amplitude of oscillations after 13 collisions is : (M = 10, m = 5, u = 1, k = 1)
JEE Main 2018 (Online) 16th April Morning Slot
86
A particle executes simple harmonic motion and is located at x = a, b and c at times t0, 2t0 and 3t0 respectively. The freqquency of the oscillation is :
JEE Main 2018 (Online) 16th April Morning Slot
87
A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 1012/sec. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver = 108 and Avogadro number = 6.02 × 1023 gm mole–1)
JEE Main 2018 (Offline)
88
Two simple harmonic motions, as shown below, are at right angles. They are combined to form Lissajous figures.
x(t) = A sin (at + $$\delta $$)
y(t) = B sin (bt)

Identify the correct match below.
JEE Main 2018 (Online) 15th April Evening Slot
89
A block of mass 0.1 kg is connected to an elastic spring of spring constant 640 Nm−1 and oscillates in a damping medium of damping constant 10−2 kg s−1 . The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to :
JEE Main 2017 (Online) 9th April Morning Slot
90
A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8 kg block placed on the same table. So, the frequency of vibration of the 8 kg block is :
JEE Main 2017 (Online) 8th April Morning Slot
91
The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10 s−1 . At, t = 0 the displacement is 5 m. What is the maximum acceleration ? The initial phase is $${\pi \over 4}$$.
JEE Main 2017 (Online) 8th April Morning Slot
92
A particle is executing simple harmonic motion with a time period T. At time t = 0, it is at its position of equilibrium. The kinetic energy – time graph of the particle will look like:
JEE Main 2017 (Offline)
93
In an engine the piston undergoes vertical simple harmonic motion with amplitude 7 cm. A washer rests on top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer no longer stays in contact with the piston, is close to :
JEE Main 2016 (Online) 10th April Morning Slot
94
Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to A and I, respectively. At time t = 0 one particle has displacement A while the other one has displacement $${{ - A} \over 2}$$ and they are moving towards each other. If they cross each other at time t, then t is :
JEE Main 2016 (Online) 9th April Morning Slot
95
A particle performs simple harmonic motion with amplitude $$A.$$ Its speed is trebled at the instant that it is at a distance $${{2A} \over 3}$$ from equilibrium position. The new amplitude of the motion is:
JEE Main 2016 (Offline)
96
A pendulum made of a uniform wire of cross sectional area $$A$$ has time period $$T.$$ When an additional mass $$M$$ is added to its bob, the time period changes to $${T_{M.}}$$ If the Young's modulus of the material of the wire is $$Y$$ then $${1 \over Y}$$ is equal to :
($$g=$$ $$gravitational$$ $$acceleration$$)
JEE Main 2015 (Offline)
97
For a simple pendulum, a graph is plotted between its kinetic energy $$(KE)$$ and potential energy $$(PE)$$ against its displacement $$d.$$ Which one of the following represents these correctly?
$$(graphs$$ $$are$$ $$schematic$$ $$and$$ $$not$$ $$drawn$$ $$to$$ $$scale)$$
JEE Main 2015 (Offline)
98
The period of oscillation of a simple pendulum is $$T = 2\pi \sqrt {{L \over g}} $$. Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using wrist watch of 1 s resolution. The accuracy in the determination of g is:
JEE Main 2015 (Offline)
99
A particle moves with simple harmonic motion in a straight line. In first $$\tau s,$$ after starting from rest it travels a distance $$a,$$ and in next $$\tau s$$ it travels $$2a,$$ in same direction, then:
JEE Main 2014 (Offline)
100
An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $$M.$$ The piston and the cylinder have equal cross sectional area $$A$$. When the piston is in equilibrium, the volume of the gas is $${V_0}$$ and its pressure is $${P_0}.$$ The piston is slightly displaced from the equilibrium position and released,. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frquency
JEE Main 2013 (Offline)
101
The amplitude of a damped oscillator decreases to $$0.9$$ times its original magnitude in $$5s$$. In another $$10s$$ it will decrease to $$\alpha $$ times its original magnitude, where $$\alpha $$ equals
JEE Main 2013 (Offline)
102
If a simple pendulum has significant amplitude (up to a factor of $$1/e$$ of original ) only in the period between $$t = 0s\,\,to\,\,t = \tau \,s,$$ then $$\tau \,$$ may be called the average life of the pendulum When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity with $$b$$ as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds :
AIEEE 2012
103
A mass $$M,$$ attached to a horizontal spring, executes $$S.H.M.$$ with amplitude $${A_1}.$$ When the mass $$M$$ passes through its mean position then a smaller mass $$m$$ is placed over it and both of them move together with amplitude $${A_2}.$$ The ratio of $$\left( {{{{A_1}} \over {{A_2}}}} \right)$$ is :
AIEEE 2011
104
Two particles are executing simple harmonic motion of the same amplitude $$A$$ and frequency $$\omega $$ along the $$x$$-axis. Their mean position is separated by distance $${X_0}\left( {{X_0} > A} \right)$$. If the maximum separation between them is $$\left( {{X_0} + A} \right),$$ the phase difference between their motion is:
AIEEE 2011
105
If $$x,$$ $$v$$ and $$a$$ denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period $$T,$$ then, which of the following does not change with time?
AIEEE 2009
106
A particle of mass $$m$$ executes simple harmonic motion with amplitude a and frequency $$v.$$ The average kinetic energy during its motion from the position of equilibrium to the end is
AIEEE 2007
107
Two springs, of force constant $${k_1}$$ and $${k_2}$$ are connected to a mass $$m$$ as shown. The frequency of oscillation of the mass is $$f.$$ If both $${k_1}$$ and $${k_2}$$ are made four times their original values, the frequency of oscillation becomes AIEEE 2007 Physics - Simple Harmonic Motion Question 146 English
AIEEE 2007
108
A point mass oscillates along the $$x$$-axis according to the law $$x = {x_0}\,\cos \left( {\omega t - \pi /4} \right).$$ If the acceleration of the particle is written as $$a = A\,\cos \left( {\omega t + \delta } \right),$$ then
AIEEE 2007
109
The displacement of an object attached to a spring and executing simple harmonic motion is given by $$x = 2 \times {10^{ - 2}}$$ $$cos$$ $$\pi t$$ metre. The time at which the maximum speed first occurs is
AIEEE 2007
110
The maximum velocity of a particle, executing simple harmonic motion with an amplitude $$7$$ $$mm,$$ is $$4.4$$ $$m/s.$$ The period of oscillation is
AIEEE 2006
111
A coin is placed on a horizontal platform which undergoes vertical simple harmonic motoin of angular frequency $$\omega .$$ The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time
AIEEE 2006
112
Starting from the origin a body oscillates simple harmonically with a period of $$2$$ $$s.$$ After what time will its kinetic energy be $$75\% $$ of the total energy?
AIEEE 2006
113
If a simple harmonic motion is represented by $${{{d^2}x} \over {d{t^2}}} + \alpha x = 0.$$ its time period is
AIEEE 2005
114
The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would
AIEEE 2005
115
Two simple harmonic motions are represented by the equations $${y_1} = 0.1\,\sin \left( {100\pi t + {\pi \over 3}} \right)$$ and $${y_2} = 0.1\,\cos \,\pi t.$$ The phase difference of the velocity of particle $$1$$ with respect to the velocity of particle $$2$$ is
AIEEE 2005
116
The function $${\sin ^2}\left( {\omega t} \right)$$ represents
AIEEE 2005
117
The bob of a simple pendulum executes simple harmonic motion in water with a period $$t,$$ while the period of oscillation of the bob is $${t_0}$$ in air. Neglecting frictional force of water and given that the density of the bob is $$\left( {4/3} \right) \times 1000\,\,kg/{m^3}.$$ What relationship between $$t$$ and $${t_0}$$ is true
AIEEE 2004
118
A particle at the end of a spring executes $$S.H.M$$ with a period $${t_1}$$. While the corresponding period for another spring is $${t_2}$$. If the period of oscillation with the two springs in series is $$T$$ then
AIEEE 2004
119
The total energy of particle, executing simple harmonic motion is
AIEEE 2004
120
In forced oscillation of a particle the amplitude is maximum for a frequency $${\omega _1}$$ of the force while the energy is maximum for a frequency $${\omega _2}$$ of the force; then
AIEEE 2004
121
A particle of mass $$m$$ is attached to a spring (of spring constant $$k$$) and has a natural angular frequency $${\omega _0}.$$ An external force $$F(t)$$ proportional to $$\cos \,\omega t\left( {\omega \ne {\omega _0}} \right)$$ is applied to the oscillator. The time displacement of the oscillator will be proportional to
AIEEE 2004
122
A mass $$M$$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes $$SHM$$ of time period $$T.$$ If the mass is increased by $$m.$$ the time period becomes $${{5T} \over 3}$$. Then the ratio of $${{m} \over M}$$ is
AIEEE 2003
123
Two particles $$A$$ and $$B$$ of equal masses are suspended from two massless springs of spring of spring constant $${k_1}$$ and $${k_2}$$, respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of $$A$$ and $$B$$ is
AIEEE 2003
124
The displacement of particle varies according to the relation
$$x=4$$$$\left( {\cos \,\pi t + \sin \,\pi t} \right).$$ The amplitude of the particle is
AIEEE 2003
125
The length of a simple pendulum executing simple harmonic motion is increased by $$21\% $$. The percentage increase in the time period of the pendulum of increased length is
AIEEE 2003
126
A body executes simple harmonic motion. The potential energy $$(P.E),$$ the kinetic energy $$(K.E)$$ and total energy $$(T.E)$$ are measured as a function of displacement $$x.$$ Which of the following statements is true ?
AIEEE 2003
127
If a spring has time period $$T,$$ and is cut into $$n$$ equal parts, then the time period of each part will be
AIEEE 2002
128
In a simple harmonic oscillator, at the mean position
AIEEE 2002
129
A child swinging on a swing in sitting position, stands up, then the time period of the swing will
AIEEE 2002

Numerical

1

A particle of mass $$0.50 \mathrm{~kg}$$ executes simple harmonic motion under force $$F=-50(\mathrm{Nm}^{-1}) x$$. The time period of oscillation is $$\frac{x}{35} s$$. The value of $$x$$ is _________.

(Given $$\pi=\frac{22}{7}$$)

JEE Main 2024 (Online) 9th April Evening Shift
2

The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of $$4 \mathrm{~m}, 2 \mathrm{~ms}^{-1}$$ and $$16 \mathrm{~ms}^{-2}$$ at a certain instant. The amplitude of the motion is $$\sqrt{x}, \mathrm{~m}$$ where $$x$$ is _________.

JEE Main 2024 (Online) 9th April Morning Shift
3

An object of mass $$0.2 \mathrm{~kg}$$ executes simple harmonic motion along $$x$$ axis with frequency of $$\left(\frac{25}{\pi}\right) \mathrm{Hz}$$. At the position $$x=0.04 \mathrm{~m}$$ the object has kinetic energy $$0.5 \mathrm{~J}$$ and potential energy $$0.4 \mathrm{~J}$$. The amplitude of oscillation is ________ $$\mathrm{cm}$$.

JEE Main 2024 (Online) 8th April Evening Shift
4

A particle is doing simple harmonic motion of amplitude $$0.06 \mathrm{~m}$$ and time period $$3.14 \mathrm{~s}$$. The maximum velocity of the particle is _________ $$\mathrm{cm} / \mathrm{s}$$.

JEE Main 2024 (Online) 6th April Morning Shift
5

The displacement of a particle executing SHM is given by $$x=10 \sin \left(w t+\frac{\pi}{3}\right) m$$. The time period of motion is $$3.14 \mathrm{~s}$$. The velocity of the particle at $$t=0$$ is _______ $$\mathrm{m} / \mathrm{s}$$.

JEE Main 2024 (Online) 4th April Evening Shift
6
A mass $m$ is suspended from a spring of negligible mass and the system oscillates with a frequency $f_1$. The frequency of oscillations if a mass $9 \mathrm{~m}$ is suspended from the same spring is $f_2$. The value of $\frac{f_1}{f_2} \mathrm{i}$ ________.
JEE Main 2024 (Online) 1st February Evening Shift
7

The time period of simple harmonic motion of mass $$M$$ in the given figure is $$\pi \sqrt{\frac{\alpha M}{5 k}}$$, where the value of $$\alpha$$ is _________.

JEE Main 2024 (Online) 31st January Evening Shift Physics - Simple Harmonic Motion Question 23 English

JEE Main 2024 (Online) 31st January Evening Shift
8

A particle performs simple harmonic motion with amplitude $$A$$. Its speed is increased to three times at an instant when its displacement is $$\frac{2 A}{3}$$. The new amplitude of motion is $$\frac{n A}{3}$$. The value of $$n$$ is ___________.

JEE Main 2024 (Online) 31st January Morning Shift
9

A simple harmonic oscillator has an amplitude $$A$$ and time period $$6 \pi$$ second. Assuming the oscillation starts from its mean position, the time required by it to travel from $$x=$$ A to $$x=\frac{\sqrt{3}}{2}$$ A will be $$\frac{\pi}{x} \mathrm{~s}$$, where $$x=$$ _________.

JEE Main 2024 (Online) 29th January Evening Shift
10

When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is $$\frac{x}{8}$$, where $$x=$$ _________.

JEE Main 2024 (Online) 29th January Morning Shift
11

A particle executes simple harmonic motion with an amplitude of $$4 \mathrm{~cm}$$. At the mean position, velocity of the particle is $$10 \mathrm{~cm} / \mathrm{s}$$. The distance of the particle from the mean position when its speed becomes $$5 \mathrm{~cm} / \mathrm{s}$$ is $$\sqrt{\alpha} \mathrm{~cm}$$, where $$\alpha=$$ ________.

JEE Main 2024 (Online) 27th January Morning Shift
12

At a given point of time the value of displacement of a simple harmonic oscillator is given as $$\mathrm{y}=\mathrm{A} \cos \left(30^{\circ}\right)$$. If amplitude is $$40 \mathrm{~cm}$$ and kinetic energy at that time is $$200 \mathrm{~J}$$, the value of force constant is $$1.0 \times 10^{x} ~\mathrm{Nm}^{-1}$$. The value of $$x$$ is ____________.

JEE Main 2023 (Online) 13th April Morning Shift
13

A rectangular block of mass $$5 \mathrm{~kg}$$ attached to a horizontal spiral spring executes simple harmonic motion of amplitude $$1 \mathrm{~m}$$ and time period $$3.14 \mathrm{~s}$$. The maximum force exerted by spring on block is _________ N

JEE Main 2023 (Online) 10th April Evening Shift
14

A simple pendulum with length $$100 \mathrm{~cm}$$ and bob of mass $$250 \mathrm{~g}$$ is executing S.H.M. of amplitude $$10 \mathrm{~cm}$$. The maximum tension in the string is found to be $$\frac{x}{40} \mathrm{~N}$$. The value of $$x$$ is ___________.

JEE Main 2023 (Online) 6th April Evening Shift
15

The amplitude of a particle executing SHM is $$3 \mathrm{~cm}$$. The displacement at which its kinetic energy will be $$25 \%$$ more than the potential energy is: __________ $$\mathrm{cm}$$

JEE Main 2023 (Online) 1st February Morning Shift
16

In the figure given below, a block of mass $$M=490 \mathrm{~g}$$ placed on a frictionless table is connected with two springs having same spring constant $$\left(\mathrm{K}=2 \mathrm{~N} \mathrm{~m}^{-1}\right)$$. If the block is horizontally displaced through '$$\mathrm{X}$$' $$\mathrm{m}$$ then the number of complete oscillations it will make in $$14 \pi$$ seconds will be _____________.

JEE Main 2023 (Online) 31st January Morning Shift Physics - Simple Harmonic Motion Question 46 English

JEE Main 2023 (Online) 31st January Morning Shift
17
The velocity of a particle executing SHM varies with displacement $(x)$ as $4 v^{2}=50-x^{2}$. The time period of oscillations is $\frac{x}{7} s$. The value of $x$ is ___________. $\left(\right.$ Take $\left.\pi=\frac{22}{7}\right)$
JEE Main 2023 (Online) 30th January Evening Shift
18

The general displacement of a simple harmonic oscillator is $$x = A\sin \omega t$$. Let T be its time period. The slope of its potential energy (U) - time (t) curve will be maximum when $$t = {T \over \beta }$$. The value of $$\beta$$ is ______________.

JEE Main 2023 (Online) 30th January Morning Shift
19

A particle of mass 250 g executes a simple harmonic motion under a periodic force $$\mathrm{F}=(-25~x)\mathrm{N}$$. The particle attains a maximum speed of 4 m/s during its oscillation. The amplitude of the motion is ___________ cm.

JEE Main 2023 (Online) 29th January Evening Shift
20

A mass m attached to free end of a spring executes SHM with a period of 1s. If the mass is increased by 3 kg the period of the oscillation increases by one second, the value of mass m is ___________ kg.

JEE Main 2023 (Online) 24th January Evening Shift
21

JEE Main 2023 (Online) 24th January Morning Shift Physics - Simple Harmonic Motion Question 38 English

A block of a mass 2 kg is attached with two identical springs of spring constant 20 N/m each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is $$\frac{\pi}{\sqrt x}$$ in SI unit. The value of $$x$$ is ____________.

JEE Main 2023 (Online) 24th January Morning Shift
22

The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is $$10 \mathrm{~s}$$. If the metallic bob is immersed in water, then the new time period becomes $$5 \sqrt{x}$$ s. The value of $$x$$ will be ________.

JEE Main 2022 (Online) 29th July Evening Shift
23

The potential energy of a particle of mass $$4 \mathrm{~kg}$$ in motion along the x-axis is given by $$\mathrm{U}=4(1-\cos 4 x)$$ J. The time period of the particle for small oscillation $$(\sin \theta \simeq \theta)$$ is $$\left(\frac{\pi}{K}\right) s$$. The value of $$\mathrm{K}$$ is _________.

JEE Main 2022 (Online) 28th July Evening Shift
24

A mass $$0.9 \mathrm{~kg}$$, attached to a horizontal spring, executes SHM with an amplitude $$\mathrm{A}_{1}$$. When this mass passes through its mean position, then a smaller mass of $$124 \mathrm{~g}$$ is placed over it and both masses move together with amplitude $$A_{2}$$. If the ratio $$\frac{A_{1}}{A_{2}}$$ is $$\frac{\alpha}{\alpha-1}$$, then the value of $$\alpha$$ will be ___________.

JEE Main 2022 (Online) 27th July Morning Shift
25

As per given figures, two springs of spring constants $$k$$ and $$2 k$$ are connected to mass $$m$$. If the period of oscillation in figure (a) is $$3 \mathrm{s}$$, then the period of oscillation in figure (b) will be $$\sqrt{x}~ s$$. The value of $$x$$ is ___________.

JEE Main 2022 (Online) 26th July Evening Shift Physics - Simple Harmonic Motion Question 55 English

JEE Main 2022 (Online) 26th July Evening Shift
26

A body is performing simple harmonic with an amplitude of 10 cm. The velocity of the body was tripled by air jet when it is at 5 cm from its mean position. The new amplitude of vibration is $$\sqrt{x}$$ cm. The value of x is _____________.

JEE Main 2022 (Online) 29th June Morning Shift
27

A pendulum is suspended by a string of length 250 cm. The mass of the bob of the pendulum is 200 g. The bob is pulled aside until the string is at 60$$^\circ$$ with vertical as shown in the figure. After releasing the bob, the maximum velocity attained by the bob will be ____________ ms$$-$$1. (if g = 10 m/s2)

JEE Main 2022 (Online) 28th June Morning Shift Physics - Simple Harmonic Motion Question 63 English

JEE Main 2022 (Online) 28th June Morning Shift
28

A particle executes simple harmonic motion. Its amplitude is 8 cm and time period is 6 s. The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is ___________ s.

JEE Main 2022 (Online) 27th June Evening Shift
29
A particle of mass 1 kg is hanging from a spring of force constant 100 Nm$$-$$1. The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period T. The time when the kinetic energy and potential energy of the system will become equal, is $${T \over x}$$. The value of x is _____________.
JEE Main 2021 (Online) 31st August Morning Shift
30
Two simple harmonic motion, are represented by the equations $${y_1} = 10\sin \left( {3\pi t + {\pi \over 3}} \right)$$ $${y_2} = 5(\sin 3\pi t + \sqrt 3 \cos 3\pi t)$$ Ratio of amplitude of y1 to y2 = x : 1. The value of x is ______________.
JEE Main 2021 (Online) 27th August Evening Shift
31
Two simple harmonic motions are represented by the equations

$${x_1} = 5\sin \left( {2\pi t + {\pi \over 4}} \right)$$ and $${x_2} = 5\sqrt 2 (\sin 2\pi t + \cos 2\pi t)$$. The amplitude of second motion is ................ times the amplitude in first motion.
JEE Main 2021 (Online) 26th August Evening Shift
32
A particle executes simple harmonic motion represented by displacement function as

x(t) = A sin($$\omega$$t + $$\phi$$)

If the position and velocity of the particle at t = 0 s are 2 cm and 2$$\omega$$ cm s$$-$$1 respectively, then its amplitude is $$x\sqrt 2 $$ cm where the value of x is _________________.
JEE Main 2021 (Online) 27th July Evening Shift
33
In the reported figure, two bodies A and B of masses 200 g and 800 g are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be ____________ rad/s when k = 20 N/m.

JEE Main 2021 (Online) 25th July Morning Shift Physics - Simple Harmonic Motion Question 79 English
JEE Main 2021 (Online) 25th July Morning Shift
34
A pendulum bob has a speed of 3 m/s at its lowest position. The pendulum is 50 cm long. The speed of bob, when the length makes an angle of 60$$^\circ$$ to the vertical will be (g = 10 m/s2) ____________ m/s.
JEE Main 2021 (Online) 25th July Morning Shift
35
A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is $${1 \over a}$$s. The value of 'a' to the nearest integer is _________.
JEE Main 2021 (Online) 18th March Morning Shift
36
Consider two identical springs each of spring constant k and negligible mass compared to the mass M as shown. Fig. 1 shows one of them and Fig. 2 shows their series combination. The ratios of time period of oscillation of the two SHM is Tb/Ta = $$\sqrt x $$, where value of x is ___________. (Round off to the Nearest Integer)

JEE Main 2021 (Online) 17th March Morning Shift Physics - Simple Harmonic Motion Question 88 English
JEE Main 2021 (Online) 17th March Morning Shift
37
A particle executes S.H.M. with amplitude 'a', and time period 'T'. The displacement of the particle when its speed is half of maximum speed is $${{\sqrt x a} \over 2}$$. The value of x is __________.
JEE Main 2021 (Online) 26th February Evening Shift
38
Time period of a simple pendulum is T. The time taken to complete $${5 \over 8}$$ oscillations starting from mean position is $${\alpha \over \beta }T$$. The value of $$\alpha$$ is _________.
JEE Main 2021 (Online) 26th February Evening Shift
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