Simple Harmonic Motion PYQs - Last 10 Years

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Practice 55 AP EAPCET 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 55 filtered questions.

1Simple Harmonic Motion

The amplitude of a damped harmonic oscilator becomes $50 \%$ of its initial value in a time of 12 s . If the amplitude of the oscillator at a time of 36 s is $x \%$ of its initial amplitude, then the value of $x$ is

2Simple Harmonic Motion

If the displacement of a particle executing simple harmonic motion is given by $x=0.5 \cos (125.6 t)$, then the time period of oscillation of the particle is nearly (Here, $x$ is displacement in metre and $t$ is time in second)

3Simple Harmonic Motion

On a smooth inclined plane a block of mass $M$ is fixed to two rigid supports using two springs as shown in the figure. If each spring has spring constant $k$, then the period of oscillation of the block is
(Neglect the masses of the spring...

4Simple Harmonic Motion

If the function $\sin ^2 \omega t$ ( $t$ is time in second) represents a periodic motion, then the period of the motion is

5Simple Harmonic Motion

A particle is executing simple harmonic motion with amplitude $A$. The ratio of the kinetic energies of the particle when it is at displacements of $\frac{A}{4}$ and $\frac{A}{2}$ from the mean position is

6Simple Harmonic Motion

A particle is executing simple harmonic motion starting from its mean position. If the time period of the particle is 1.5 s , then the minimum time at which the ratio of the kinetic and total energies of the particle becomes 3:4 is

7Simple Harmonic Motion

A body of mass 4 kg attached to a spring of force constant $64 \mathrm{Nm}^{-1}$ executes simple harmonic motion on a frictionless horizontal surface. The time period of oscillation is

8Simple Harmonic Motion

A particle is executing simple harmonic motion with amplitude $A$. At a distance ' $x$ ' from the mean position, when the particle is moving towards extreme position it receives a blow in the direction of motion which instantaneously double...

9Simple Harmonic Motion

A spring is stretched by 0.2 m when a mass of 0.5 kg is suspended to it. The time period of the spring when 0.5 kg mass is replaced with a mass of 0.25 kg is suspended to it is
(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

10Simple Harmonic Motion

The equations for the displacements of two particles in simple harmonic motion are $y_1=0.1 \sin \left(100 \pi t+\frac{\pi}{3}\right)$ and $y_2=0.1 \cos \pi t$ respectively. The phase difference between the velocities of the two particles a...

11Simple Harmonic Motion

For a particle executing simple harmonic motion, the ratio of kinetic and potential energies at a point where displacement is one half of the amplitude is

12Simple Harmonic Motion

When the mass attached to a spring is increased from 4 kg to 9 kg , the time period of oscillation increases by $0.2 \pi \mathrm{~s}$. Then, the spring constant of the spring is

13Simple Harmonic Motion

A body of mass 1 kg is suspended from a spring of force constant $600 \mathrm{Nm}^{-1}$. Another body of mass 0.5 kg moving vertically upwards hits the suspended body with a velocity of $3 \mathrm{~ms}^{-1}$ and embedded in it. The amplitud...

14Simple Harmonic Motion

If the maximum velocity and maximum acceleration of a particle executing simple harmonic motion are respectively $5 \mathrm{~ms}^{-1}$ and $10 \mathrm{~ms}^{-2}$, then the time period of oscillation of the particle is

15Simple Harmonic Motion

If the displacement ' $x$ ' of a body in motion in terms of time ' $t$ ' is given by $x=A \sin (\omega t+\theta)$, then the minimum time at which the displacement becomes maximum is

16Simple Harmonic Motion

A body of mass 1 kg is attached to the lower end of a vertically suspended spring of force constant $600 \mathrm{~N}-\mathrm{m}^{-1}$. If another body of mass 0.5 kg moving vertically upward hits the suspended body with a velocity $3 \mathr...

17Simple Harmonic Motion

The kinetic energy of a particle executing simple harmonic motion at a displacement of 3 cm from the mean position is 4 mJ . If the amplitude of the particle is 5 cm , then the maximum force acting on the particle is

18Simple Harmonic Motion

If the displacement $y$ (in cm ) of a particle executing simple harmonic motion is given by the equation $y=5 \sin (3 \pi t)+5 \sqrt{3} \cos (3 \pi t)$, then the amplitude of the particle is

19Simple Harmonic Motion

The angular frequency of a block of mass 0.1 kg oscillating with the help of a spring of force constant $2.5 \mathrm{~N}-\mathrm{m}^{-1}$ is

20Simple Harmonic Motion

As shown in the figure, two blocks of masses $m_1$ and $m_2$ are connected to spring of force constant $k$. The blocks are slightly displaced in opposite directions to $x_1, x_2$ distances and released. If the system executes simple harmoni...

21Simple Harmonic Motion

A mass $M$, attached to a horizontal spring executes simple harmonic motion with amplitude $A_1$. When mass $M$ passes mean position, then a smaller mass millis attached to it and both of them together executing simple harmonic motion with ...

22Simple Harmonic Motion

When a mass $m$ is connected individually to the springs $k_1$ and $k_2$, the oscillation frequencies are $v_1$ and $v_2$. If the same mass is attached to the two springs as shown in the figure, the oscillation frequency would be

23Simple Harmonic Motion

One bar magnet is in simple harmonic motion with time period $T$ in an earth's magnetic field. If its mass is increased by 9 times the time period becomes

24Simple Harmonic Motion

Two simple harmonic motions are represented by $y_1=5[\sin 2 \pi t+\sqrt{3} \cos 2 \pi t]$ and $y_2=5 \sin \left[2 \pi t+\frac{\pi}{4}\right]$. The ratio of their amplitudes is

25Simple Harmonic Motion

The displacement of a particle of mass 2 g executing simple harmonic motion is $x=8 \cos \left(50 t+\frac{\pi}{12}\right) \mathrm{m}$, where $t$ is time in second. The maximum kinetic energy of the particle is

26Simple Harmonic Motion

The relation between the force ( $F$ in Newton) acting on a particle executing simple harmonic motion and the displacement of the particle ( $y$ in metre) is $500 F+\pi^2 y=0$. If the mass of the particle is 2 g . The time period of oscilla...

27Simple Harmonic Motion

The potential energy of a particle of mass 10 g as a function of displacement $x$ is $\left(50 x^2+100\right) \mathrm{J}$. The frequency of oscillation is

28Simple Harmonic Motion

The mass of a particle is 1 kg and it is moving along $X$-axis. The period of its oscillation is $\frac{\pi}{2}$. Its potential energy at a displacement of 0.2 m is

29Simple Harmonic Motion

In a spring block system as shown in figure. If the spring constant $k=9 \pi^2 \mathrm{Nm}^{-1}$, then the time period of oscillation is

30Simple Harmonic Motion

A body is executing simple harmonic motion. At a displacement $x$ its potential energy is $E_1$ and at a displacement $y$ its potential energy is $E_2$. The potential energy $E$ at a displacement $(x+y)$ is

31Simple Harmonic Motion

A 3 kg block is connected as shown in the figure. Spring constants of two springs $k_1$ and $k_2$ are $50 \mathrm{Nm}^{-1}$ and $150 \mathrm{Nm}^{-1}$ respectively. The block is released from rest with the springs unstretched. The accelerat...

32Simple Harmonic Motion

A particle is executing simple harmonic motion with a time period of 3 s . At a position where the displacement of the particle is $60 \%$ of its amplitude. The ratio of the kinetic and potential energies of the particle is

33Simple Harmonic Motion

In a time of 2 s , the amplitude of a damped oscillator becomes $\frac{1}{e}$ times, its initial amplitude $A$. In the next two second, the amplitude of the oscillator is

34Simple Harmonic Motion

A horizontal board is performing simple harmonic oscillations horizontally with an amplitude 0.3 m and a period of 4 s . The minimum coefficient of friction between a heavy body placed on the board if the body does not slip will be

35Simple Harmonic Motion

A test tube of mass 6 g and uniform area of cross-section $10 \mathrm{~cm}^2$ is floating in water vertically when 10 g of mercury is in the bottom. The tube is depressed by a small amount and then released. The time period of oscillation i...

36Simple Harmonic Motion

The displacement of a particle executing simple harmonic motion is $y=A \sin (2 t+\phi) \mathrm{m}$, where $t$ is time in second and $\phi$ is phase angle. At time $t=0$, the displacement and velocity of the particle are 2 m and $4 \mathrm{...

37Simple Harmonic Motion

The displacement of a damped oscillator is $x(t)=\exp (-0.2 t) \cos (3.2 t+\phi)$, where $t$ is time in second The time requirement for the amplitude of the oscillator to become $\frac{1}{e^{1.2}}$ times its initial amplitude is

38Simple Harmonic Motion

For a particle executing simple harmonic motion, Match the following statements ( conditions) from Column I to statements (shapes of graph) in Columinit .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-sty...

39Simple Harmonic Motion

Time period of a simple pendulum in air is $T$. If the pendulum is in water and executes SHM. Its time period is $t$. The value of $\frac{T}{t}$ is. (density of bob is $\frac{5000}{3} \mathrm{~kg} \mathrm{~m}^{-3}$ )

40Simple Harmonic Motion

The amplitudes of a damped harmonic oscillator after 2 and 4 seconds are $A_1$ and $A_2$ respectively. If the initial amplitude of the oscillator is $A_0$, then

41Simple Harmonic Motion

As shown in the figure, a block of weight 20 N is connected to the top of a smooth inclined plane by massless spring of constant $8 \pi^2 \mathrm{Nm}^{-1}$. If the block is pulled slightly from its mean position and released, the period of ...

42Simple Harmonic Motion

An object of mass 3 kg is executing simple harmonic motion with an amplitude $\frac{2}{\pi} \mathrm{~m}$. If the kinetic energy of the object when it crosses the mean position is 6 J , the time period of oscillation of the object is

43Simple Harmonic Motion

If the amplitude of a lightly damped oscillator decreases by \(1.5 \%\) then the mechanical energy of the oscillator lost in each cycle is

44Simple Harmonic Motion

A particle is executing simple harmonic motion with an instantaneous displacement \(x=A \sin ^2\left(\omega t-\frac{\pi}{4}\right)\). The time period of oscillation of the particle is

45Simple Harmonic Motion

A cone with half the density of water is floating in water as shown in figure. It is depressed down by a small distance \(\delta(\ll< H)\) and released. The frequency of simple harmonic oscillations of the cone is

46Simple Harmonic Motion

A hydrometer executes simple harmonic motion when it is pushed down vertically in a liquid of density \(\rho\). If the mass of hydrometer is \(m\) and the radius of the hydrometer tube is \(r\), then the time period of oscillation is

47Simple Harmonic Motion

An object undergoing simple harmonic motion takes 0.5 s to travel from one point of zero velocity to the next such point. The angular frequency of the motion is

48Simple Harmonic Motion

A body is executing S.H.M. At a displacement \(x\) its potential energy is 9 J and at a displacement \(y\) its potential energy is 16 J . The potential energy at displacement \((x+y)\) is

49Simple Harmonic Motion

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

50Simple Harmonic Motion

A particle executing simple harmonic motion
along a straight line with an amplitude A,
attains maximum potential energy when its
displacement from mean position equals