# Simple Harmonic Motion · Physics · JEE Main

Start Practice## Numerical

JEE Main 2024 (Online) 9th April Evening Shift

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 ...

JEE Main 2024 (Online) 9th April Morning Shift

The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of $$4 \mathrm{~m}, 2 \mathrm{~ms}...

JEE Main 2024 (Online) 8th April Evening Shift

An object of mass $$0.2 \mathrm{~kg}$$ executes simple harmonic motion along $$x$$ axis with frequency of $$\left(\frac{25}{\pi}\right) \mathrm{Hz}$$....

JEE Main 2024 (Online) 6th April Morning Shift

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 particl...

JEE Main 2024 (Online) 4th April Evening Shift

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{~...

JEE Main 2024 (Online) 1st February Evening Shift

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 ...

JEE Main 2024 (Online) 31st January Evening Shift

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 Morning Shift

A particle performs simple harmonic motion with amplitude $$A$$. Its speed is increased to three times at an instant when its displacement is $$\frac{...

JEE Main 2024 (Online) 29th January Evening Shift

A simple harmonic oscillator has an amplitude $$A$$ and time period $$6 \pi$$ second. Assuming the oscillation starts from its mean position, the time...

JEE Main 2024 (Online) 29th January Morning Shift

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}$...

JEE Main 2024 (Online) 27th January Morning Shift

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...

JEE Main 2023 (Online) 13th April Morning Shift

At a given point of time the value of displacement of a simple harmonic oscillator is given as $$\mathrm{y}=\mathrm{A} \cos \left(30^{\circ}\right)$$....

JEE Main 2023 (Online) 10th April Evening Shift

A rectangular block of mass $$5 \mathrm{~kg}$$ attached to a horizontal spiral spring executes simple harmonic motion of amplitude $$1 \mathrm{~m}$$ a...

JEE Main 2023 (Online) 6th April Evening Shift

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 maxim...

JEE Main 2023 (Online) 1st February Morning Shift

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

JEE Main 2023 (Online) 31st January Morning Shift

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 const...

JEE Main 2023 (Online) 30th January Evening Shift

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...

JEE Main 2023 (Online) 30th January Morning Shift

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) - ...

JEE Main 2023 (Online) 29th January Evening Shift

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 spe...

JEE Main 2023 (Online) 24th January Evening Shift

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 b...

JEE Main 2023 (Online) 24th January Morning Shift

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 e...

JEE Main 2022 (Online) 29th July Evening Shift

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 immerse...

JEE Main 2022 (Online) 28th July Evening Shift

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 o...

JEE Main 2022 (Online) 27th July Morning Shift

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 mea...

JEE Main 2022 (Online) 26th July Evening Shift

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...

JEE Main 2022 (Online) 29th June Morning Shift

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 posi...

JEE Main 2022 (Online) 28th June Morning Shift

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$...

JEE Main 2022 (Online) 27th June Evening Shift

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...

JEE Main 2021 (Online) 31st August Morning Shift

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...

JEE Main 2021 (Online) 27th August Evening Shift

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 + \sq...

JEE Main 2021 (Online) 26th August Evening Shift

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...

JEE Main 2021 (Online) 27th July Evening Shift

A particle executes simple harmonic motion represented by displacement function as x(t) = A sin($$\omega$$t + $$\phi$$)If the position and velocity of...

JEE Main 2021 (Online) 25th July Morning Shift

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...

JEE Main 2021 (Online) 25th July Morning Shift

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...

JEE Main 2021 (Online) 18th March Morning Shift

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 ampl...

JEE Main 2021 (Online) 17th March Morning Shift

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 show...

JEE Main 2021 (Online) 26th February Evening Shift

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 $${{\s...

JEE Main 2021 (Online) 26th February Evening Shift

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 }...

## MCQ (Single Correct Answer)

JEE Main 2024 (Online) 5th April Morning Shift

A simple pendulum doing small oscillations at a place $$R$$ height above earth surface has time period of $$T_1=4 \mathrm{~s}$$. $$\mathrm{T}_2$$ woul...

JEE Main 2024 (Online) 4th April Evening Shift

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 ...

JEE Main 2024 (Online) 1st February Morning Shift

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 ...

JEE Main 2024 (Online) 29th January Evening Shift

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 ini...

JEE Main 2024 (Online) 27th January Evening Shift

A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. T...

JEE Main 2023 (Online) 15th April Morning Shift

In a linear Simple Harmonic Motion (SHM)
(A) Restoring force is directly proportional to the displacement.
(B) The acceleration and displacement ar...

JEE Main 2023 (Online) 13th April Evening Shift

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 Morning Shift

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) 12th April Morning Shift

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

JEE Main 2023 (Online) 11th April Morning Shift

The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement $$(x)$$ starting from mean position to extre...

JEE Main 2023 (Online) 10th April Morning Shift

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...

JEE Main 2023 (Online) 8th April Evening Shift

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...

JEE Main 2023 (Online) 6th April Morning Shift

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...

JEE Main 2023 (Online) 1st February Evening Shift

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) 31st January Morning Shift

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

JEE Main 2023 (Online) 30th January Evening Shift

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 f...

JEE Main 2023 (Online) 25th January Evening Shift

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...

JEE Main 2023 (Online) 25th January Morning Shift

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) abo...

JEE Main 2022 (Online) 29th July Morning Shift

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 pl...

JEE Main 2022 (Online) 28th July Evening Shift

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...

JEE Main 2022 (Online) 26th July Morning Shift

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

JEE Main 2022 (Online) 25th July Morning Shift

In figure $$(\mathrm{A})$$, mass '$$2 \mathrm{~m}^{\text {' }}$$ is fixed on mass '$$\mathrm{m}$$ ' which is attached to two springs of spring consta...

JEE Main 2022 (Online) 29th June Evening Shift

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 se...

JEE Main 2022 (Online) 28th June Morning Shift

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...

JEE Main 2022 (Online) 27th June Evening Shift

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 pa...

JEE Main 2022 (Online) 27th June Morning Shift

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 h...

JEE Main 2022 (Online) 26th June Morning Shift

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 wil...

JEE Main 2022 (Online) 24th June Evening Shift

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 tha...

JEE Main 2021 (Online) 1st September Evening Shift

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 sim...

JEE Main 2021 (Online) 31st August Evening Shift

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...

JEE Main 2021 (Online) 31st August Evening Shift

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...

JEE Main 2021 (Online) 27th August Morning Shift

The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure.The potential energy U(x) versus ti...

JEE Main 2021 (Online) 27th July Evening Shift

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 ...

JEE Main 2021 (Online) 27th July Morning Shift

A particle starts executing simple harmonic motion (SHM) of amplitude 'a' and total energy E. At any instant, its kinetic energy is $${{3E} \over 4}$$...

JEE Main 2021 (Online) 25th July Evening Shift

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 ...

JEE Main 2021 (Online) 22th July Evening Shift

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 ...

JEE Main 2021 (Online) 20th July Evening Shift

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...

JEE Main 2021 (Online) 18th March Evening Shift

The function of time representing a simple harmonic motion with a period of $${\pi \over \omega }$$ is :

JEE Main 2021 (Online) 18th March Morning Shift

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 1...

JEE Main 2021 (Online) 17th March Evening Shift

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 du...

JEE Main 2021 (Online) 17th March Evening Shift

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. De...

JEE Main 2021 (Online) 17th March Morning Shift

For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal ?

JEE Main 2021 (Online) 16th March Evening Shift

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 muc...

JEE Main 2021 (Online) 16th March Morning Shift

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 o...

JEE Main 2021 (Online) 26th February Evening Shift

A particle executes S.H.M., the graph of velocity as a function of displacement is :

JEE Main 2021 (Online) 26th February Evening Shift

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 b...

JEE Main 2021 (Online) 26th February Morning Shift

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 Eart...

JEE Main 2021 (Online) 26th February Morning Shift

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) 25th February Evening Shift

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...

JEE Main 2021 (Online) 25th February Evening Shift

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 equ...

JEE Main 2021 (Online) 25th February Evening Shift

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 projec...

JEE Main 2021 (Online) 25th February Morning Shift

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) 24th February Evening Shift

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 f...

JEE Main 2021 (Online) 24th February Evening Shift

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

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 ...

JEE Main 2021 (Online) 24th February Morning Shift

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...

JEE Main 2020 (Online) 6th September Evening Slot

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, ...

JEE Main 2020 (Online) 3rd September Evening Slot

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 m...

JEE Main 2020 (Online) 2nd September Evening Slot

The displacement time graph of a particle
executing S.H.M is given in figure :(sketch is
schematic and not to scale)
Which of the following statement...

JEE Main 2020 (Online) 9th January Evening Slot

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 fixe...

JEE Main 2020 (Online) 8th January Evening Slot

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 s...

JEE Main 2019 (Online) 10th April Morning Slot

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 amplit...

JEE Main 2019 (Online) 8th April Evening Slot

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 i...

JEE Main 2019 (Online) 12th January Evening Slot

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 ar...

JEE Main 2019 (Online) 12th January Morning Slot

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...

JEE Main 2019 (Online) 11th January Evening Slot

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 s...

JEE Main 2019 (Online) 11th January Evening Slot

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 i...

JEE Main 2019 (Online) 11th January Evening Slot

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 h...

JEE Main 2019 (Online) 11th January Morning Slot

A particle undergoing simple harmonic motion has time dependent displacement given by x(t) = Asin$${{\pi t} \over {90}}$$. The ratio of kinetic to pot...

JEE Main 2019 (Online) 10th January Evening Slot

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...

JEE Main 2019 (Online) 10th January Evening Slot

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 sligh...

JEE Main 2019 (Online) 10th January Evening Slot

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 veloci...

JEE Main 2019 (Online) 9th January Evening Slot

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 ener...

JEE Main 2019 (Online) 9th January Evening Slot

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 ...

JEE Main 2018 (Online) 16th April Morning Slot

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 rig...

JEE Main 2018 (Online) 16th April Morning Slot

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 ...

JEE Main 2018 (Offline)

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 ...

JEE Main 2018 (Online) 15th April Evening Slot

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) =...

JEE Main 2017 (Online) 9th April Morning Slot

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...

JEE Main 2017 (Online) 8th April Morning Slot

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 a...

JEE Main 2017 (Online) 8th April Morning Slot

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 a...

JEE Main 2017 (Offline)

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 gr...

JEE Main 2016 (Online) 10th April Morning Slot

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 moto...

JEE Main 2016 (Online) 9th April Morning Slot

Two particles are performing simple harmonic motion in a straight line about
the same equilibrium point. The amplitude and time period for both partic...

JEE Main 2016 (Offline)

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 ...

JEE Main 2015 (Offline)

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 f...

JEE Main 2015 (Offline)

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 per...

JEE Main 2015 (Offline)

For a simple pendulum, a graph is plotted between its kinetic energy $$(KE)$$ and potential energy $$(PE)$$ against its displacement $$d.$$ Which one ...

JEE Main 2014 (Offline)

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 nex...

JEE Main 2013 (Offline)

The amplitude of a damped oscillator decreases to $$0.9$$ times its original magnitude in $$5s$$. In another $$10s$$ it will decrease to $$\alpha $$ ...

JEE Main 2013 (Offline)

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 ...

AIEEE 2012

If a simple pendulum has significant amplitude (up to a factor of $$1/e$$ of original ) only in the period between $$t = 0s\,\,to\,\,t = \tau \,s,$$ t...

AIEEE 2011

Two particles are executing simple harmonic motion of the same amplitude $$A$$ and frequency $$\omega $$ along the $$x$$-axis. Their mean position is ...

AIEEE 2011

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...

AIEEE 2009

If $$x,$$ $$v$$ and $$a$$ denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period $$T...

AIEEE 2007

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 b...

AIEEE 2007

A particle of mass $$m$$ executes simple harmonic motion with amplitude a and frequency $$v.$$ The average kinetic energy during its motion from the p...

AIEEE 2007

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 p...

AIEEE 2007

The displacement of an object attached to a spring and executing simple harmonic motion is given by $$x = 2 \times {10^{ - 2}}$$ $$cos$$ $$\pi t$$ met...

AIEEE 2006

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motoin of angular frequency $$\omega .$$ The amplitude of oscillati...

AIEEE 2006

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 t...

AIEEE 2006

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 2005

The function $${\sin ^2}\left( {\omega t} \right)$$ represents

AIEEE 2005

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 ...

AIEEE 2005

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 unplugg...

AIEEE 2005

If a simple harmonic motion is represented by $${{{d^2}x} \over {d{t^2}}} + \alpha x = 0.$$ its time period is

AIEEE 2004

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 ...

AIEEE 2004

The total energy of particle, executing simple harmonic motion is

AIEEE 2004

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 p...

AIEEE 2004

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...

AIEEE 2004

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 ...

AIEEE 2003

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 ...

AIEEE 2003

Two particles $$A$$ and $$B$$ of equal masses are suspended from two massless springs of spring of spring constant $${k_1}$$ and $${k_2}$$, respectiv...

AIEEE 2003

The length of a simple pendulum executing simple harmonic motion is increased by $$21\% $$. The percentage increase in the time period of the pendulum...

AIEEE 2003

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 func...

AIEEE 2003

The displacement of particle varies according to the relation
$$x=4$$$$\left( {\cos \,\pi t + \sin \,\pi t} \right).$$ The amplitude of the particle ...

AIEEE 2002

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

In a simple harmonic oscillator, at the mean position

AIEEE 2002

A child swinging on a swing in sitting position, stands up, then the time period of the swing will