Simple Harmonic Motion · Physics · AP EAPCET

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MCQ (Single Correct Answer)

1

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 harmonic motion, then the frequency of oscillation of the system ( $\omega$ ) is

AP EAPCET 2024 - 23th May Morning Shift Physics - Simple Harmonic Motion Question 1 English
AP EAPCET 2024 - 23th May Morning Shift
2
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 amplitude $A_2$. Then, value of $\frac{A_1}{A_2}$ is
AP EAPCET 2024 - 23th May Morning Shift
3

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

AP EAPCET 2024 - 22th May Evening Shift
4
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 oscillation of the particle is
AP EAPCET 2024 - 22th May Evening Shift
5

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

AP EAPCET 2024 - 22th May Morning Shift
6

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

AP EAPCET 2024 - 22th May Morning Shift Physics - Simple Harmonic Motion Question 5 English
AP EAPCET 2024 - 22th May Morning Shift
7

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

AP EAPCET 2024 - 22th May Morning Shift
8

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

AP EAPCET 2024 - 21th May Evening Shift Physics - Simple Harmonic Motion Question 8 English
AP EAPCET 2024 - 21th May Evening Shift
9
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
AP EAPCET 2024 - 21th May Evening Shift
10
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
AP EAPCET 2024 - 21th May Morning Shift
11
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
AP EAPCET 2024 - 21th May Morning Shift
12
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
AP EAPCET 2024 - 20th May Evening Shift
13
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 is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )
AP EAPCET 2024 - 20th May Evening Shift
14

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 acceleration of the block in its lowest position is $\left(g=10 \mathrm{~ms}^{-2}\right)$

AP EAPCET 2024 - 20th May Morning Shift Physics - Simple Harmonic Motion Question 14 English
AP EAPCET 2024 - 20th May Morning Shift
15
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
AP EAPCET 2024 - 20th May Morning Shift
16
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
AP EAPCET 2024 - 20th May Morning Shift
17
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 $4 \mathrm{~ms}^{-1}$. The phase angle, $\phi=$
AP EAPCET 2024 - 19th May Evening Shift
18
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
AP EAPCET 2024 - 19th May Evening Shift
19
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 $\frac{5000}{3} \mathrm{~kg} \mathrm{~m}^{-3}$ )
AP EAPCET 2024 - 18th May Morning Shift
20
For a particle executing simple harmonic motion, Match the following statements ( conditions) from Column I to statements (shapes of graph) in Columinit
Column I Column II
a Velocity-displacement graph
$(\omega=1)$
i Straight line
b Acceleration-displacement graph ii Sinusoidal
c Acceleration - time graph iii Circle
d Acceleration - velocity $(\omega \neq 1)$ iv Ellipse
AP EAPCET 2024 - 18th May Morning Shift
21

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

AP EAPCET 2022 - 5th July Morning Shift
22

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

AP EAPCET 2022 - 5th July Morning Shift
23

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

AP EAPCET 2022 - 4th July Evening Shift
24

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

AP EAPCET 2022 - 4th July Morning Shift
25

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

AP EAPCET 2022 - 4th July Morning Shift
26

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

AP EAPCET 2022 - 4th July Morning Shift Physics - Simple Harmonic Motion Question 24 English

AP EAPCET 2022 - 4th July Morning Shift
27

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

AP EAPCET 2021 - 20th August Morning Shift
28

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

AP EAPCET 2021 - 20th August Morning Shift
29

A block of mass $$\mathrm{l} \mathrm{kg}$$ is fastened to a spring of spring constant of $$100 ~\mathrm{Nm}^{-1}$$. The block is pulled to a distance $$x=10 \mathrm{~cm}$$ from its equilibrium position $$(x=0 \mathrm{~cm})$$ on a frictionless surface, from rest at $$t=0$$. The kinetic energy and the potential energy of the block when it is $$5 \mathrm{~cm}$$ away from the mean position is

AP EAPCET 2021 - 19th August Evening Shift
30

The scale of a spring balance which can measure from 0 to $$15 \mathrm{~kg}$$ is $$0.25 \mathrm{~m}$$ long. If a body suspended from this balance oscillates with a time period $$\frac{2 \pi}{5} \mathrm{~s}$$, neglecting the mass of the spring, find the mass of the body suspended.

AP EAPCET 2021 - 19th August Evening Shift
31

A spring is stretched by 0.40 m when a mass of 0.6 kg is suspended from it. The period of oscillations of the spring loaded by 255 g and put to oscillations is close to (g = 10 ms$$^{-2}$$)

AP EAPCET 2021 - 19th August Morning Shift
32

A heavy brass sphere is hung from a spring and it executes vertical vibrations with period T. The sphere is now immersed in a non-viscous liquid with a density (1/10 )th that of brass. When set into vertical vibrations with the sphere remaining inside liquid all the time, the time period will be

AP EAPCET 2021 - 19th August Morning Shift
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