Simple Harmonic Motion PYQs - Last 10 Years

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Practice 144 JEE Main Physics questions from Simple Harmonic Motion. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Last 10 Years Simple Harmonic Motion Questions

Showing 50 of 144 filtered questions.

1Simple Harmonic Motion

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

2Simple Harmonic Motion

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...

INTEGER+4 / -12023

3Simple Harmonic Motion

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.

INTEGER+4 / -12023

4Simple Harmonic Motion

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: __________ \(\mathrm{cm}\)

INTEGER+4 / -12023

5Simple Harmonic Motion

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

6Simple Harmonic Motion

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 accelerat...

7Simple Harmonic Motion

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}...

INTEGER+4 / -12023

8Simple Harmonic Motion

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

9Simple Harmonic Motion

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 :

10Simple Harmonic Motion

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

11Simple Harmonic Motion

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

12Simple Harmonic Motion

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 o...

13Simple Harmonic Motion

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 _____...

INTEGER+4 / -12023

14Simple Harmonic Motion

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 _____________.

INTEGER+4 / -12022

15Simple Harmonic Motion

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

16Simple Harmonic Motion

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 :

17Simple Harmonic Motion

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 ...

INTEGER+4 / -12022

18Simple Harmonic Motion

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 veloc...

INTEGER+4 / -12022

19Simple Harmonic Motion

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 :

20Simple Harmonic Motion

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}...

INTEGER+4 / -12022

21Simple Harmonic Motion

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 re...

22Simple Harmonic Motion

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 :

23Simple Harmonic Motion

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.

INTEGER+4 / -12022

24Simple Harmonic Motion

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)

25Simple Harmonic Motion

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 m...

INTEGER+4 / -12022

26Simple Harmonic Motion

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)

27Simple Harmonic Motion

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

28Simple Harmonic Motion

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 v...

INTEGER+4 / -12022

29Simple Harmonic Motion

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 spri...

30Simple Harmonic Motion

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 ...

31Simple Harmonic Motion

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 pote...

INTEGER+4 / -12021

32Simple Harmonic Motion

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...

33Simple Harmonic Motion

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 increas...

34Simple Harmonic Motion

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 :

35Simple Harmonic Motion

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 amplit...

INTEGER+4 / -12021

36Simple Harmonic Motion

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...

37Simple Harmonic Motion

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 is correctly shown in figure :

38Simple Harmonic Motion

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 ____________...

INTEGER+4 / -12021

39Simple Harmonic Motion

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 wi...

40Simple Harmonic Motion

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 :

41Simple Harmonic Motion

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

42Simple Harmonic Motion

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 _________.

INTEGER+4 / -12021

43Simple Harmonic Motion

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 __________.

INTEGER+4 / -12021

44Simple Harmonic Motion

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 ...

45Simple Harmonic Motion

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 ampli...

INTEGER+4 / -12021

46Simple Harmonic Motion

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.

INTEGER+4 / -12021

47Simple Harmonic Motion

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 ...

INTEGER+4 / -12021

48Simple Harmonic Motion

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.

49Simple Harmonic Motion

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 :

50Simple Harmonic Motion

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 res...