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JEE Main

Simple Harmonic Motion

Physics

Previous Years Questions

Numerical

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The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is $$10 \mathrm{~s}$$. ...
JEE Main 2022 (Online) 29th July Evening Shift
The potential energy of a particle of mass $$4 \mathrm{~kg}$$ in motion along the x-axis is given by $$\mathrm{U}=4(1-\c...
JEE Main 2022 (Online) 28th July Evening Shift
A mass $$0.9 \mathrm{~kg}$$, attached to a horizontal spring, executes SHM with an amplitude $$\mathrm{A}_{1}$$. When th...
JEE Main 2022 (Online) 27th July Morning Shift
As per given figures, two springs of spring constants $$k$$ and $$2 k$$ are connected to mass $$m$$. If the period of os...
JEE Main 2022 (Online) 26th July Evening Shift
A particle executes simple harmonic motion. Its amplitude is 8 cm and time period is 6 s. The time it will take to trave...
JEE Main 2022 (Online) 27th June Evening Shift
A pendulum is suspended by a string of length 250 cm. The mass of the bob of the pendulum is 200 g. The bob is pulled as...
JEE Main 2022 (Online) 28th June Morning Shift
A body is performing simple harmonic with an amplitude of 10 cm. The velocity of the body was tripled by air jet when it...
JEE Main 2022 (Online) 29th June Morning Shift
A particle of mass 1 kg is hanging from a spring of force constant 100 Nm$$-$$1. The mass is pulled slightly downward an...
JEE Main 2021 (Online) 31st August Morning Shift
Two simple harmonic motion, are represented by the equations $${y_1} = 10\sin \left( {3\pi t + {\pi \over 3}} \right)$$...
JEE Main 2021 (Online) 27th August Evening Shift
Two simple harmonic motions are represented by the equations $${x_1} = 5\sin \left( {2\pi t + {\pi \over 4}} \right)$$ ...
JEE Main 2021 (Online) 26th August Evening Shift
A particle executes simple harmonic motion represented by displacement function as x(t) = A sin($$\omega$$t + $$\phi$$)I...
JEE Main 2021 (Online) 27th July Evening Shift
A pendulum bob has a speed of 3 m/s at its lowest position. The pendulum is 50 cm long. The speed of bob, when the lengt...
JEE Main 2021 (Online) 25th July Morning Shift
A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displace...
JEE Main 2021 (Online) 18th March Morning Shift
Consider two identical springs each of spring constant k and negligible mass compared to the mass M as shown. Fig. 1 sho...
JEE Main 2021 (Online) 17th March Morning Shift
Time period of a simple pendulum is T. The time taken to complete $${5 \over 8}$$ oscillations starting from mean positi...
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 h...
JEE Main 2021 (Online) 26th February Evening Shift
A uniform metallic wire is elongated by 0.04 m when subjected to a linear force F. The elongation, if its length and dia...
JEE Main 2021 (Online) 24th February Evening Slot

MCQ (Single Correct Answer)

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The time period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle, which moves withou...
JEE Main 2022 (Online) 29th 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) 26th July Morning Shift
In figure $$(\mathrm{A})$$, mass '$$2 \mathrm{~m}^{\text {' }}$$ is fixed on mass '$$\mathrm{m}$$ ' which is attached t...
JEE Main 2022 (Online) 25th July Morning Shift
Time period of a simple pendulum in a stationary lift is 'T'. If the lift accelerates with $${g \over 6}$$ vertically up...
JEE Main 2022 (Online) 26th June Morning Shift
The displacement of simple harmonic oscillator after 3 seconds starting from its mean position is equal to half of its a...
JEE Main 2022 (Online) 27th June Morning Shift
The equation of a particle executing simple harmonic motion is given by $$x = \sin \pi \left( {t + {1 \over 3}} \right)m...
JEE Main 2022 (Online) 27th June Evening Shift
Motion of a particle in x-y plane is described by a set of following equations $$x = 4\sin \left( {{\pi \over 2} - \ome...
JEE Main 2022 (Online) 28th June Morning Shift
The motion of a simple pendulum executing S.H.M. is represented by the following equation. $$y = A\sin (\pi t + \phi )$$...
JEE Main 2022 (Online) 29th June 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...
JEE Main 2021 (Online) 1st September 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 ov...
JEE Main 2021 (Online) 31st August Evening Shift
The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure.The p...
JEE Main 2021 (Online) 27th August Morning 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 wi...
JEE Main 2021 (Online) 27th July Evening Shift
A particle starts executing simple harmonic motion (SHM) of amplitude 'a' and total energy E. At any instant, its kineti...
JEE Main 2021 (Online) 27th July Morning Shift
In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the pa...
JEE Main 2021 (Online) 25th July Evening Shift
T0 is the time period of a simple pendulum at a place. if the length of the pendulum is reduced to $${1 \over {16}}$$ ti...
JEE Main 2021 (Online) 22th July Evening Shift
Consider a binary star system of star A and star B with masses mA and mB revolving in a circular orbit of radii rA an rB...
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 vel...
JEE Main 2021 (Online) 20th July 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 Evening 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 ...
JEE Main 2021 (Online) 18th March Morning 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 a...
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...
JEE Main 2021 (Online) 17th March Evening Shift
Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass = 500g, Decay ...
JEE Main 2021 (Online) 16th March Evening Shift
Time period of a simple pendulum is T inside a lift when the lift is stationary. If the lift moves upwards with an accel...
JEE Main 2021 (Online) 16th March Morning Shift
Given below are two statements :Statement I : A second's pendulum has a time period of 1 second.Statement II : It takes ...
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
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...
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 ...
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...
JEE Main 2021 (Online) 25th February Evening Shift
If the time period of a two meter long simple pendulum is 2s, the acceleration due to gravity at the place where pendulu...
JEE Main 2021 (Online) 25th February Morning Slot
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 Slot
In the given figure, a body of mass M is held between two massless springs, on a smooth inclined plane. The free ends of...
JEE Main 2021 (Online) 24th February 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...
JEE Main 2020 (Online) 6th September Evening Slot
In a resonance tube experiment when the tube is filled with water up to a height of 17.0 cm from bottom, it resonates wi...
JEE Main 2020 (Online) 5th September Morning Slot
A block of mass m attached to a massless spring is performing oscillatory motion of amplitude ‘A’ on a frictionless hori...
JEE Main 2020 (Online) 3rd 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) Wh...
JEE Main 2020 (Online) 2nd September Evening Slot
Two identical strings X and Z made of same material have tension TX and TZ in them. If their fundamental frequencies are...
JEE Main 2020 (Online) 2nd September Morning Slot
A wire of length L and mass per unit length 6.0 × 10–3 kgm–1 is put under tension of 540 N. Two consecutive frequencies ...
JEE Main 2020 (Online) 9th January Evening Slot
A simple pendulum is being used to determine th value of gravitational acceleration g at a certain place. Th length of t...
JEE Main 2020 (Online) 8th 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 an...
JEE Main 2019 (Online) 12th January Evening Slot
Two light identical springs of spring constant k are attached horizontally at the two ends of a uniform horizontal rod A...
JEE Main 2019 (Online) 12th January Morning Slot
A travelling harmonic wave is represented by the equation y(x,t) = 10–3sin (50t + 2x), where, x and y are in mater and t...
JEE Main 2019 (Online) 12th January Morning Slot
A pendulum is executing simple harmonic motion and its maximum kinetic energy is K1. If the length of the pendulum is do...
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 os...
JEE Main 2019 (Online) 11th January Evening Slot
A particle undergoing simple harmonic motion has time dependent displacement given by x(t) = Asin$${{\pi t} \over {90}}$...
JEE Main 2019 (Online) 11th January Morning Slot
A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean positio...
JEE Main 2019 (Online) 10th January Evening Slot
A cylindrical plastic bottle of negligible mass is filled with 310 ml of water and left floating in a pond with still wa...
JEE Main 2019 (Online) 10th January Evening Slot
A closed organ pipe has a fundamental frequency of 1.5 kHz. The number of overtones that can be distinctly heard by a pe...
JEE Main 2019 (Online) 10th January Evening Slot
A particle is executing simple harmonic motion (SHM) of amplitude A, along the x-axis, about x = 0. When its potential E...
JEE Main 2019 (Online) 9th January Evening Slot
A particle executes simple harmonic motion and is located at x = a, b and c at times t0, 2t0 and 3t0 respectively. The ...
JEE Main 2018 (Online) 16th April Morning Slot
An oscillator of mass M is at rest in its equilibrium position in a potential V = $${1 \over 2}$$ k(x $$-$$ X)2. A par...
JEE Main 2018 (Online) 16th April Morning Slot
Two simple harmonic motions, as shown below, are at right angles. They are combined to form Lissajous figures. x(t) = A...
JEE Main 2018 (Online) 15th April Evening Slot
A thin uniform tube is bent into a circle of radius $$r$$ in the vertical plane. Equal volumes of two immiscible liquids...
JEE Main 2018 (Online) 15th April Morning Slot
A block of mass 0.1 kg is connected to an elastic spring of spring constant 640 Nm−1 and oscillates in a damping medium ...
JEE Main 2017 (Online) 9th April Morning Slot
The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10 s−1 . At, t = 0 the displacement...
JEE Main 2017 (Online) 8th April Morning Slot
A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs iden...
JEE Main 2017 (Online) 8th April Morning Slot
In an engine the piston undergoes vertical simple harmonic motion with amplitude 7 cm. A washer rests on top of the pist...
JEE Main 2016 (Online) 10th April Morning Slot
Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude a...
JEE Main 2016 (Online) 9th April Morning Slot
A particle performs simple harmonic motion with amplitude $$A.$$ Its speed is trebled at the instant that it is at a dis...
JEE Main 2016 (Offline)
For a simple pendulum, a graph is plotted between its kinetic energy $$(KE)$$ and potential energy $$(PE)$$ against its ...
JEE Main 2015 (Offline)
A pendulum made of a uniform wire of cross sectional area $$A$$ has time period $$T.$$ When an additional mass $$M$$ is ...
JEE Main 2015 (Offline)
A particle moves with simple harmonic motion in a straight line. In first $$\tau s,$$ after starting from rest it travel...
JEE Main 2014 (Offline)
An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $$M.$$ The piston and ...
JEE Main 2013 (Offline)
The amplitude of a damped oscillator decreases to $$0.9$$ times its original magnitude in $$5s$$. In another $$10s$$ it ...
JEE Main 2013 (Offline)
If a simple pendulum has significant amplitude (up to a factor of $$1/e$$ of original ) only in the period between $$t =...
AIEEE 2012
A mass $$M,$$ attached to a horizontal spring, executes $$S.H.M.$$ with amplitude $${A_1}.$$ When the mass $$M$$ passes ...
AIEEE 2011
Two particles are executing simple harmonic motion of the same amplitude $$A$$ and frequency $$\omega $$ along the $$x$$...
AIEEE 2011
If $$x,$$ $$v$$ and $$a$$ denote the displacement, the velocity and the acceleration of a particle executing simple harm...
AIEEE 2009
The displacement of an object attached to a spring and executing simple harmonic motion is given by $$x = 2 \times {10^{...
AIEEE 2007
A point mass oscillates along the $$x$$-axis according to the law $$x = {x_0}\,\cos \left( {\omega t - \pi /4} \right).$...
AIEEE 2007
A particle of mass $$m$$ executes simple harmonic motion with amplitude a and frequency $$v.$$ The average kinetic energ...
AIEEE 2007
Two springs, of force constant $${k_1}$$ and $${k_2}$$ are connected to a mass $$m$$ as shown. The frequency of oscillat...
AIEEE 2007
The maximum velocity of a particle, executing simple harmonic motion with an amplitude $$7$$ $$mm,$$ is $$4.4$$ $$m/s.$$...
AIEEE 2006
Starting from the origin a body oscillates simple harmonically with a period of $$2$$ $$s.$$ After what time will its ki...
AIEEE 2006
A coin is placed on a horizontal platform which undergoes vertical simple harmonic motoin of angular frequency $$\omega ...
AIEEE 2006
If a simple harmonic motion is represented by $${{{d^2}x} \over {d{t^2}}} + \alpha x = 0.$$ its time period is
AIEEE 2005
The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscilla...
AIEEE 2005
Two simple harmonic motions are represented by the equations $${y_1} = 0.1\,\sin \left( {100\pi t + {\pi \over 3}} \rig...
AIEEE 2005
The function $${\sin ^2}\left( {\omega t} \right)$$ represents
AIEEE 2005
In forced oscillation of a particle the amplitude is maximum for a frequency $${\omega _1}$$ of the force while the ener...
AIEEE 2004
A particle of mass $$m$$ is attached to a spring (of spring constant $$k$$) and has a natural angular frequency $${\omeg...
AIEEE 2004
A particle at the end of a spring executes $$S.H.M$$ with a period $${t_1}$$. While the corresponding period for another...
AIEEE 2004
The total energy of particle, executing simple harmonic motion is
AIEEE 2004
The bob of a simple pendulum executes simple harmonic motion in water with a period $$t,$$ while the period of oscillati...
AIEEE 2004
The displacement of particle varies according to the relation $$x=4$$$$\left( {\cos \,\pi t + \sin \,\pi t} \right).$$ ...
AIEEE 2003
A body executes simple harmonic motion. The potential energy $$(P.E),$$ the kinetic energy $$(K.E)$$ and total energy $$...
AIEEE 2003
The length of a simple pendulum executing simple harmonic motion is increased by $$21\% $$. The percentage increase in t...
AIEEE 2003
Two particles $$A$$ and $$B$$ of equal masses are suspended from two massless springs of spring of spring constant $${k...
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 ...
AIEEE 2003
A child swinging on a swing in sitting position, stands up, then the time period of the swing will
AIEEE 2002
In a simple harmonic oscillator, at the mean position
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

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