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Oscillations — JEE Main & Advanced Physics PYQs

458 previous year questions from Oscillations with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

458 questionsPhysicsSolutions on every page
1

A tank contains two immiscible liquids of densities 6 and 2 . The higher density liquid is filled up to a height L/2 from the bottom. A thin rod of density and length L is fully im

JEE Advanced 2026 Solution View → 2

The frequency of oscillation of a mass m suspended by a spring is v₁ . If the length of the spring is cut to half, the same mass oscillates with frequency v₂ . The value of v₂/v₁ i

JEE Main 2026 Solution View → 3

A spring stretches by 2 mm when it is loaded with a mass of 200 g. From equilibrium position the mass is further pulled down by 2 mm and released. The frequency associated with the

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A particle is executing simple harmonic motion. Its amplitude is A and time period is 5 sec. The time required by it to move from x = A to x = A 2 is _______ sec.

JEE Main 2026 Solution View → 5

Match List-I with List-II. List-I List-II A. ^2 t I. Periodic with time period T = but not simple harmonic motion (SHM) B. ^3(2 t) II. Periodic with time period T = 2 but Not SHM C

JEE Main 2026 Solution View → 6

A uniform disc of radius R and mass M is free to oscillate about the axis A as shown in the figure. For small oscillations the time period is ______. ( g is acceleration due to gra

JEE Main 2026 Solution View → 7

The velocity of a particle executing simple harmonic motion along x -axis is described as v^2 = 50 - x^2 , where x represents displacement. If the time period of motion is x 7 s, t

JEE Main 2026 Solution View → 8

The equation of motion of a particle is given by x = a (50t + 3 ) cm. The particle will come to rest at time t₁ and it will have zero acceleration at time t₂ . The t₁ and t₂ respec

JEE Main 2026 Solution View → 9

The time period of a simple harmonic oscillator is T=2 k m . Measured value of mass (m) of the object is 10 g with an accuracy of 10 mg and time for 50 oscillations of the spring i

JEE Main 2026 Solution View → 10

As shown in the figure, a spring is kept in a stretched position with some extension by holding the masses 1 kg and 0.2 kg with a separation more than spring natural length and are

JEE Main 2026 Solution View → 11

The displacement of a particle, executing simple harmonic motion with time period T , is expressed as x(t)=A t , where A is the amplitude. The maximum value of potential energy of

JEE Main 2026 Solution View → 12

A cylindrical block of mass M and area of cross section A is floating in a liquid of density and with its axis vertical. When depressed a little and released the block starts oscil

JEE Main 2026 Solution View → 13

Two blocks with masses 100 g and 200 g are attached to the ends of springs A and B as shown in figure. The energy stored in A is E . The energy stored in B , when spring constants

JEE Main 2026 Solution View → 14

A simple pendulum of string length 30 cm performs 20 oscillations in 10 s. The length of the string required for the pendulum to perform 40 oscillations in the same time duration i

JEE Main 2026 Solution View → 15

Using a simple pendulum experiment g is determind by measuring its time period T . Which of the following plots represent the correct relation between the pendulum length L and tim

JEE Main 2026 Solution View → 16

The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of 176 rad / s . The frequency of this simple harmonic oscillator is _ _ _ _ Hz. [ . take .

JEE Main 2026 Solution View → 17

The center of a disk of radius r and mass m is attached to a spring of spring constant k , inside a ring of radius R>r as shown in the figure. The other end of the spring is attach

JEE Advanced 2025 Solution View → 18

As shown in the figures, a uniform rod O O^ of length l is hinged at the point O and held in place vertically between two walls using two massless springs of same spring constant.

JEE Advanced 2025 Solution View → 19

The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, y ₁( x , t )=4 ( kx - t ) and y ₂( x , t )=2 ( kx - t + 2 3 ) , are : (Take

JEE Main 2025 Solution View → 20

Two simple pendulums having lengths l₁ and l₂ with negligible string mass undergo angular displacements ₁ and ₂ , from their mean positions, respectively. If the angular accelerati

JEE Main 2025 Solution View → 21

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

JEE Main 2025 Solution View → 22

A particle is subjected two simple harmonic motions as : x ₁= 7 5 tcm and x₂=2 7 (5 t+ 3 ) cm where x is displacement and t is time in seconds. The maximum acceleration of the part

JEE Main 2025 Solution View → 23

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

JEE Main 2025 Solution View → 24

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

JEE Main 2025 Solution View → 25

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Knowing initial position x₀ and initial momentum p₀ is eno

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A particle oscillates along the x -axis according to the law, x( t )=x₀ ^2 ( t 2 ) where x₀=1 ~m . The kinetic energy ( K ) of the particle as a function of x is correctly represen

JEE Main 2025 Solution View → 27

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

JEE Main 2025 Solution View → 28

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 oscillatio

JEE Main 2025 Solution View → 29

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,

JEE Main 2025 Solution View → 30

A block of mass 5 ~kg moves along the x -direction subject to the force F=(-20 x+10) N , with the value of x in metre. At time t=0 ~s , it is at rest at position x=1 ~m . The posit

JEE Advanced 2024 Solution View → 31

A particle of mass 0.50 ~kg executes simple harmonic motion under force F=-50 ( Nm ⁻¹ ) x . The time period of oscillation is x 35 ~s . The value of x is _______ (Given = 22 7 )

JEE Main 2024 Solution View → 32

The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of 4 ~m , 2 ~ms ⁻¹ and 16 ~ms ⁻² at a certain instant. The ampli

JEE Main 2024 Solution View → 33

An object of mass 0.2 ~kg executes simple harmonic motion along x axis with frequency of ( 25 ) Hz . At the position x=0.04 ~m the object has kinetic energy 0.5 ~J and potential en

JEE Main 2024 Solution View → 34

A particle is doing simple harmonic motion of amplitude 0.06 ~m and time period 3.14 ~s . The maximum velocity of the particle is _______ cm / s .

JEE Main 2024 Solution View → 35

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 Solution View → 36

The displacement of a particle executing SHM is given by x=10 (w t+ 3 ) m . The time period of motion is 3.14 ~s . The velocity of the particle at t=0 is ______ m / s .

JEE Main 2024 Solution View → 37

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 m is suspended from the same sprin

JEE Main 2024 Solution View → 38

The time period of simple harmonic motion of mass M in the given figure is π α M 5 K , where the value of α is _______.

JEE Main 2024 Solution View → 39

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

JEE Main 2024 Solution View → 40

A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is 4 m , then the time period of

JEE Main 2024 Solution View → 41

A simple harmonic oscillator has an amplitude A and time period 6 π second. Assuming the oscillation starts from its mean position, the time required by it to travel from x = A to

JEE Main 2024 Solution View → 42

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

JEE Main 2024 Solution View → 43

A particle executes simple harmonic motion with an amplitude of 4 cm . At the mean position, velocity of the particle is 10 cm s - 1 . The distance of the particle from the mean po

JEE Main 2024 Solution View → 44

Two point-like objects of masses 20 gm and 30 gm are fixed at the two ends of a rigid massless rod of length 10 cm . This system is suspended vertically from a rigid ceiling using

JEE Advanced 2023 Solution View → 45

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

JEE Main 2023 Solution View → 46

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

JEE Main 2023 Solution View → 47

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

JEE Main 2023 Solution View → 48

At a given point of time the value of displacement of a simple harmonic oscillator is given as y = A cos 30 ° . If amplitude is 40 cm and kinetic energy at that time is 200 J

JEE Main 2023 Solution View → 49

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 Solution View → 50

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 Solution View → 51

For a periodic motion represented by the equation y = sinω t + cosω t the amplitude of the motion is

JEE Main 2023 Solution View → 52

A rectangular block of mass 5 kg attached to a horizontal spiral spring executes simple harmonic motion of amplitude 1 m and time period 3 . 14 s . The maximum force exerted by spr

JEE Main 2023 Solution View → 53

A particle executes S.H.M. of amplitude A along x -axis. At t = 0 , the position of the particle is x = A 2 and it moves along positive x -axis. The displacement of particle in tim

JEE Main 2023 Solution View → 54

For particle P revolving round the centre O with radius of circular path r and regular velocity ω , as shown in below figure, the projection of O P on the x -axis at time t is

JEE Main 2023 Solution View → 55

A simple pendulum with length 100 cm and bob of mass 250 g is executing S.H.M of amplitude 10 cm . The maximum tension in the string is found to be x 40 N . The value of x is _____

JEE Main 2023 Solution View → 56

Choose the correct length ( L ) versus square of time period ( T 2 ) ) graph for a simple pendulum executing simple harmonic motion.

JEE Main 2023 Solution View → 57

The amplitude of a particle executing SHM is 3 cm . The displacement at which its kinetic energy will be 25 % more than the potential energy is: ______ cm .

JEE Main 2023 Solution View → 58

The maximum potential energy of a block executing simple harmonic motion is 25 J . A is amplitude of oscillation. At A 2 , the kinetic energy of the block is

JEE Main 2023 Solution View → 59

In the figure given below. a block of mass M = 490   g placed on a frictionless table is connected with two springs having same spring constant ( K = 2   N   m - 1 )

JEE Main 2023 Solution View → 60

For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is 1 kg , the angular frequency is ω 1 . When the mass bloc

JEE Main 2023 Solution View → 61

The velocity of a particle executing SHM varies with displacement ( x ) as 4 v 2 = 50 – x 2 . The time period of oscillations is x 7 s . The value of x is ______. [Take &#960

JEE Main 2023 Solution View → 62

The general displacement of a simple harmonic oscillator is x = A sin ω t . Let T be its time period. The slope of its potential energy ( U ) – time ( t ) curve will be

JEE Main 2023 Solution View → 63

A particle of mass 250 g executes a simple harmonic motion under a periodic force F = ( – 25 x ) N . The particle attains a maximum speed of 4 m s - 1 during its oscillation.

JEE Main 2023 Solution View → 64

Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm . The phase differe

JEE Main 2023 Solution View → 65

A particle executes simple harmonic motion between x = – A and x = + A . If time taken by particle to go from x = 0 to A 2 is 2 s ; then time taken by particle in going from

JEE Main 2023 Solution View → 66

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

JEE Main 2023 Solution View → 67

A block of mass 2 kg is attached with two identical springs of spring constant 20 N m - 1 each. The block is placed on a frictionless surface and the ends of the springs are attach

JEE Main 2023 Solution View → 68

A particle of mass 1 kg is subjected to a force which depends on the position as F → = - k x i ^ + y j ^ kg m s - 2 with k = 1 kg s - 2 . At time t = 0 , the particle's p

JEE Advanced 2022 Solution View → 69

On a frictionless horizontal plane, a bob of mass m = 0 . 1 kg is attached to a spring with natural length l 0 = 0 . 1 m . The spring constant is k 1 = 0 . 009 N m - 1 when the len

JEE Advanced 2022 Solution View → 70

The metallic bob of simple pendulum has the relative density 5 . The time period of this pendulum is 10 s . If the metallic bob is immersed in water, then the new time period becom

JEE Main 2022 Solution View → 71

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 α , is

JEE Main 2022 Solution View → 72

The potential energy of a particle of mass 4   kg in motion along the x -axis is given by U = 4 1 - cos 4 x   J . The time period of the particle for small oscillation si

JEE Main 2022 Solution View → 73

A mass 0 . 9 kg , attached to a horizontal spring, executes SHM with an amplitude A 1 . When this mass passes through its mean position, then a smaller mass of 124 g is placed over

JEE Main 2022 Solution View → 74

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 s , then the period of oscillation in figu

JEE Main 2022 Solution View → 75

When a particle executes simple Harmonic motion, the nature of graph of velocity as function of displacement will be

JEE Main 2022 Solution View → 76

Two waves executing simple harmonic motion travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the 3 times of a

JEE Main 2022 Solution View → 77

In figure (A), mass 2 m is fixed on mass m which is attached to two springs of spring constant k . In figure (B), mass m is attached to two spring of spring constant k and 2 k . If

JEE Main 2022 Solution View → 78

The motion of a simple pendulum executing S.H.M. is represented by the following equation y = A sin π t + ϕ , where time is measured in second. The length of pendulum is

JEE Main 2022 Solution View → 79

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 vi

JEE Main 2022 Solution View → 80

The equation of a particle executing simple harmonic motion is given by x = sin π t + 1 3 m . At t = 1 s , the speed of particle will be (Given: π = 3 . 14 )

JEE Main 2022 Solution View → 81

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 co

JEE Main 2022 Solution View → 82

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 Solution View → 83

Time period of a simple pendulum in a stationary lift is T . If the lift accelerates with g 6 vertically upwards then the time period will be (Where g = acceleration due to gravity

JEE Main 2022 Solution View → 84

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 ar

JEE Main 2022 Solution View → 85

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

JEE Main 2021 Solution View → 86

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 4 times th

JEE Main 2021 Solution View → 87

For a body executing S.H.M. : (a) Potential energy is always equal to its K . E . (b) Average potential and kinetic energy over any given time interval are always equal. (c) Sum of

JEE Main 2021 Solution View → 88

A particle of mass 1 kg is hanging from a spring of force constant 100 N m - 1 . The mass is pulled slightly downward and released so that it executes free simple harmonic motion w

JEE Main 2021 Solution View → 89

Two simple harmonic motion, are represented by the equations y 1 = 10 sin 3 π t + π 3 ;    y 2 = 5 ( sin 3 π t + 3 cos 3 π t ) Ratio of amplitude of y

JEE Main 2021 Solution View → 90

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 time t plot of the particle

JEE Main 2021 Solution View → 91

Two simple harmonic motions are represented by the equations x 1 = 5 sin 2 π t + π 4 and x 2 = 5 2 ( sin 2 π t + cos 2 π t ) . The amplitude of the second motio

JEE Main 2021 Solution View → 92

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

JEE Main 2021 Solution View → 93

A particle executes simple harmonic motion represented by displacement function as x ( t ) = A sin ( ω t + ϕ ) . If the position and velocity of the particle at t = 0 s a

JEE Main 2021 Solution View → 94

A particle starts executing simple harmonic motion ( SHM ) of amplitude a and total energy E . At any instant, its kinetic energy is 3 E 4 , then its displacement y is given by:

JEE Main 2021 Solution View → 95

Two identical tennis balls each having mass m and charge q are suspended from a fixed point by threads of length l . What is the equilibrium separation when each thread makes a sma

JEE Main 2021 Solution View → 96

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 Solution View → 97

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

JEE Main 2021 Solution View → 98

A pendulum bob has a speed of 3 m s - 1 at its lowest position. The pendulum is 50 cm long. The speed of bob, when the length makes an angle of 60 ° to the vertical will be g

JEE Main 2021 Solution View → 99

T 0 is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to 1 16 times of its initial value, the modified time period is

JEE Main 2021 Solution View → 100

A particle is making simple harmonic motion along the X -axis. If at a distances x 1 and x 2 from the mean position the velocities of the particle are v 1 and v 2 , respectively. T

JEE Main 2021 Solution View → 101

The function of time representing a simple harmonic motion with a period of π ω is :

JEE Main 2021 Solution View → 102

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 i

JEE Main 2021 Solution View → 103

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 dam

JEE Main 2021 Solution View → 104

Two particles A and B of equal masses are suspended from two massless springs of spring constants K 1 and K 2 respectively.If the maximum velocities during oscillations are equal,

JEE Main 2021 Solution View → 105

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

JEE Main 2021 Solution View → 106

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. Th

JEE Main 2021 Solution View → 107

The amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass = 500 g , Decay constant = 20 g s - 1 then how much time is required f

JEE Main 2021 Solution View → 108

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 Solution View → 109

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 po

JEE Main 2021 Solution View → 110

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

JEE Main 2021 Solution View → 111

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 x A 2 . The value of x is

JEE Main 2021 Solution View → 112

Time period of a simple pendulum is T . The time taken to complete 5 8 oscillations starting from mean position is α 12 T . The value of α is _ _ _ _ _ _ .

JEE Main 2021 Solution View → 113

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 f

JEE Main 2021 Solution View → 114

Two identical springs of spring constant 2 k are attached to a block of mass m and to fixed support (see figure). When the mass is displaced from equilibrium position on either sid

JEE Main 2021 Solution View → 115

The point A moves with a uniform speed along the circumference of a circle of radius 0 . 36 m and covers 30 ° in 0 . 1 s . The perpendicular projection P from A on the diamete

JEE Main 2021 Solution View → 116

Y = A sin ω t + ϕ 0 is the time-displacement equation of a S H M . At t = 0 the displacement of the particle is Y = A 2 and it is moving along negative x -direction. Then

JEE Main 2021 Solution View → 117

If the time period of a two meter long simple pendulum is 2 s , the acceleration due to gravity at the place where pendulum is executing S.H.M. is:

JEE Main 2021 Solution View → 118

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 h

JEE Main 2021 Solution View → 119

When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is:

JEE Main 2021 Solution View → 120

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 fr

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