Genius Physics (Class 11) - For IIT-JEE and CBSE

Pradeep Kshetrapal

Chapter 11

Simple Harmonic Motion - all with Video Answers

Educators

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Chapter Questions

Problem 1

A simple harmonic oscillator has an amplitude $A$ and time period $T$. The time required by it to travel from $x=A$ to $x=A / 2$ is $\quad$ [CBSE 1992; SCRA 1996]
(a) $T / 6$
(b) $T / 4$
(c) $T / 3$
(d) $T / 2$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 2

A simple harmonic oscillator has an amplitude $A$ and time period $T$. The time required by it to travel from $x=A$ to $x=A / 2$ is $\quad$ [CBSE 1992; SCRA 1996]
(a) $T / 6$
(b) $T / 4$
(c) $T / 3$
(d) $T / 2$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 3

The motion of a particle executing S.H.M. is given by $x=0.01 \sin 100 \pi(t+.05)$. Where $x$ is in meter and time $t$ is in seconds. The time period is
(a) $0.01 \mathrm{sec}$
(b) $0.02 \mathrm{sec}$
(c) $0.1 \mathrm{sec}$
(d) $0.2 \mathrm{sec}$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 4

Two equations of two S.H.M. are $x=a \sin (\omega t-\alpha)$ and $y=b \cos (\omega t-\alpha)$. The phase difference between the two is
(a) $0^{\circ}$
(b) $\infty^{\circ}$
(c) $90^{\circ}$
(d) $180^{\circ}$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 5

A body is executing simple harmonic motion with an angular frequency $2 \mathrm{rad} / \mathrm{sec}$. The velocity of the body at $20 \mathrm{~mm}$ displacement. When the amplitude of motion is $60 \mathrm{~mm}$ is [AFMC 1998]
(a) $40 \mathrm{~mm} / \mathrm{sec}$
(b) $60 \mathrm{~mm} / \mathrm{sec}$
(c) $113 \mathrm{~mm} / \mathrm{sec}$
(d) $120 \mathrm{~mm} / \mathrm{sec}$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 6

A body executing S.H.M. has equation $y=0.30 \sin (220 t+0.64)$ in meter. Then the frequency and maximum velocity of the body is
(a) $35 \mathrm{~Hz}, 66 \mathrm{~m} / \mathrm{s}$
(b) $45 \mathrm{~Hz}, 66 \mathrm{~m} / \mathrm{s}$
(c) $58 \mathrm{~Hz}, 113 \mathrm{~m} / \mathrm{s}$
(d) $35 \mathrm{~Hz}, 132 \mathrm{~m} / \mathrm{s}$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 7

A particle starts S.H.M. from the mean position. Its amplitude is $A$ and time period is $T$. At the time when its speed is half of the maximum speed. Its displacement $y$ is
(a) $A / 2$
(b) $A / \sqrt{2}$
(c) $A \sqrt{3} / 2$
(d) $2 A / \sqrt{3}$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 8

A particle perform simple harmonic motion. The equation of its motion is $x=5 \sin \left(4 t-\frac{\pi}{6}\right)$. Where $x$ is its displacement. If the displacement of the particle is 3 units then its velocity is $\quad$ [MP PMT 1994]
(a) $2 \pi / 3$
(b) $5 \pi / 6$
(c) 20
(d) 16

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 9

A simple pendulum performs simple harmonic motion about $x=0$ with an amplitude $(A)$ and time period
(T). The speed of the pendulum at $x=\frac{A}{2}$ will be $\quad$ [MP PMT 1987]
(a) $\frac{\pi A \sqrt{3}}{T}$
(b) $\underline{\pi A}$
(c) $\pi A \sqrt{3}$
(d) $\frac{3 \pi^{2} A}{T}$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 10

A particle is executing S.H.M. if its amplitude is $2 \mathrm{~m}$ and periodic time 2 seconds. Then the maximum velocity of the particle will be
(a) $6 \pi$
(b) $4 \pi$
(c) $2 \pi$
(d) $\pi$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 11

A particle is executing S.H.M. if its amplitude is $2 \mathrm{~m}$ and periodic time 2 seconds. Then the maximum velocity of the particle will be
(a) $6 \pi$
(b) $4 \pi$
(c) $2 \pi$
(d) $\pi$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 12

A particle executes S.H.M. with a period of 6 second and amplitude of $3 \mathrm{~cm}$ its maximum speed in $\mathrm{cm} / \mathrm{sec}$ is [AIIMS 1982]
(a) $\pi / 2$
(b) $\pi$
(c) $2 \pi$
(d) $3 \pi$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 13

A body of mass $5 g m$ is executing S.H.M. about a point with amplitude $10 \mathrm{~cm}$. Its maximum velocity is 100 $\mathrm{cm} / \mathrm{sec}$. Its velocity will be $50 \mathrm{~cm} / \mathrm{sec}$, at a distance
(a) 5
(b) $5 \sqrt{2}$
(c) $5 \sqrt{3}$
(d) $10 \sqrt{2}$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 14

A particle is executing simple harmonic motion with frequency $f$. The frequency at which its kinetic energy changes into potential energy is
(a) $f / 2$
(b) $f$
(c) $2 f$
(d) $4 f$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 15

When the potential energy of a particle executing simple harmonic motion is one-fourth of the maximum value during the oscillation, its displacement from the equilibrium position in terms of amplitude ' $a$ ' is(a) $a / 4$
(b) $a / 3$
(c) $a / 2$
(d) $2 a / 3$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 16

A particle of mass 10 grams is executing S.H.M. with an amplitude of o.5 meter and circular frequenc of 10 radian $/ \mathrm{sec}$. The maximum value of the force acting on the particle during the course of oscillatio:
is
[MP PMT 200
(a) $25 N$
(b) $5 N$
(c) $2.5 N$
(d) $0.5 N$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 17

A body is moving in a room with a velocity of $20 \mathrm{~m} / \mathrm{s}$ perpendicular to the two walls separated by 5 meters. There is no friction and the collision with the walls are elastic. The motion of the body is [MP PMT 19
(a) Not periodic
(b) Periodic but not simple harmonic
(c) Periodic and simple harmonic
(d) Periodic with variable time period

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 18

Two particles executes S.H.M. of same amplitude and frequency along the same straight line. They pass one another when going in opposite directions. Each time their displacement is half of their amplitude. The phase difference between them is
(a) $30^{\circ}$
(b) $60^{\circ}$
(c) $90^{\circ}$
(d) $120^{\circ}$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 19

The acceleration of a particle performing S.H.M. is $12 \mathrm{~cm} / \mathrm{sec}^{2}$ at a distance of $3 \mathrm{~cm}$ from the mean position. Its time period is
(a) $0.5 \mathrm{sec}$
(b) $1.0 \mathrm{sec}$
(c) $2.0 \mathrm{sec}$
(d) $3.14 \mathrm{sec}$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 20

A particle of mass $10 \mathrm{gm}$ is describing S.H.M. along a straight line with period of 2 sec and amplitude of $10 \mathrm{~cm}$. Its kinetic energy when it is at $5 \mathrm{~cm}$. From its equilibrium position is
(a) $37.5 \pi^{2}$ erg
(b) $3.75 \pi^{2} \mathrm{erg}$
(c) $375 \pi^{2}$ erg
(d) $0.375 \pi^{2} e r g$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 21

The total energy of the body executing S.H.M. is $E$. Then the kinetic energy when the displacement is half of the amplitude is
(a) $E / 2$
(b) $E / 4$
(c) $3 E / 4$
(d) $\sqrt{3} E / 4$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 22

The total energy of the body executing S.H.M. is $E$. Then the kinetic energy when the displacement is half of the amplitude is
(a) $E / 2$
(b) $E / 4$
(c) $3 E / 4$
(d) $\sqrt{3} E / 4$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 23

The displacement of an oscillating particle varies with time (in seconds) according to the equation. $y(c m)=\sin \frac{\pi}{2}\left(\frac{t}{2}+\frac{1}{3}\right)$. The maximum acceleration of the particle approximately
(a) $5.21 \mathrm{~cm} / \mathrm{sec}^{2}$
(b) $3.62 \mathrm{~cm} / \mathrm{sec}^{2}$
(c) $1.81 \mathrm{~cm} / \mathrm{sec}^{2}$
(d) $0.62 \mathrm{~cm} / \mathrm{sec}^{2}$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 24

The potential energy of a particle executing S.H.M. at a distance $x$ from the mean position is proportional to
[Roorkee 1992]
(a) $\sqrt{x}$
(b) $x$
(c) $x^{2}$
(d) $x^{3}$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 25

The potential energy of a particle executing S.H.M. at a distance $x$ from the mean position is proportional to
[Roorkee 1992]
(a) $\sqrt{x}$
(b) $x$
(c) $x^{2}$
(d) $x^{3}$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 26

The phase of a particle executing S.H.M. is $\frac{\pi}{2}$ when it has
(a) Maximum velocity
(b) Maximum acceleration
(c) Maximum energy
(d)

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 27

The displacement of a particle moving in S.H.M. at any instant is given by $y=a \sin \omega t$. The acceleration after time $t=\frac{T}{4}$ is (where $T$ is the time period)
(a) $a \omega$
(b) $-a \omega$
(c) $a \omega^{2}$
(d) $-a \omega^{2}$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 28

A particle of mass $m$ is hanging vertically by an ideal spring of force constant $k$, if the mass is made to oscillate vertically, its total energy is
(a) Maximum at extreme position
(b) Maximum at mean position
$\begin{array}{lll}\text { (c) Minimum at mean position } & \text { (d) } & \text { Same at all position }\end{array}$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 29

A particle moves such that its acceleration $a$ is given by $a=-b x$. Where $x$ is the displacement from equilibrium position and $\mathrm{b}$ is a constant. The period of oscillation is [NCERT 1984; CPMT 1991; MP PMT 1994; MNR 1995]
(a) $2 \pi \sqrt{b}$
(b) $\frac{2 \pi}{\sqrt{b}}$
(c) $\frac{2 \pi}{b}$
(d) $2 \sqrt{\frac{\pi}{b}}$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 30

The equation of motion of a particle is $\frac{d^{2} y}{d t^{2}}+k y=0$ where $k$ is a positive constant. The time period of the motion is given by
(a) $\frac{2 \pi}{k}$
(b) $2 \pi k$
(c) $\frac{2 \pi}{\sqrt{k}}$
(d) $2 \pi \sqrt{k}$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 31

A clock which keeps correct time at $20^{\circ} \mathrm{C}$, is subjected to $40^{\circ} \mathrm{C}$. If coefficient of linear expansion of the pendulum is $12 \times 10^{-6} /{ }^{\circ} \mathrm{C}$. How much will it gain or loose in time
(a) $10.3 \mathrm{sec} / \mathrm{day}$
(b) $20.6 \mathrm{sec} /$ day
(c) $5 \mathrm{sec} / \mathrm{day}$
(d) $20 \mathrm{~min} / \mathrm{day}$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 32

The metallic bob of simple pendulum has the relative density $\rho$. The time period of this pendulum is $T$. If the metallic bob is immersed in water, then the new time period is given by
(a) $T\left(\frac{\rho-1}{\rho}\right)$
(b) $T\left(\frac{\rho}{\rho-1}\right)$
(c) $T \sqrt{\frac{\rho-1}{\rho}}$
(d) $T \sqrt{\frac{\rho}{\rho-1}}$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 33

The period of a simple pendulum is doubled when [CPMT 1974; MNR 1980 ; AFMC 1995$]$
(a) Its length is doubled
(b) The mass of the bob is doubled
(c) Its length is made four times
(d) The mass of the bob and the length of the pendulum are doubled

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 34

A simple pendulum is executing S.H.M. with a time period $T$. if the length of the pendulum is increased by $21 \%$ the percentage increase in the time period of the pendulum is
(a) $10 \%$
(b) $21 \%$
(c) $30 \%$
(d) $50 \%$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 35

The length of simple pendulum is increased by $1 \%$ its time period will
(a) Increase by $1 \%$
(b) Increase by $0.5 \%$
(c) Decrease by 0.5\%
(d) Increase by $2 \%$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 36

The bob of a simple pendulum of mass $m$ and total energy $E$ will have maximum linear momentum equal to
[MP PMT 1986]
(a) $\sqrt{\frac{2 E}{m}}$
(b) $\sqrt{2 m E}$
(c) $2 m E$
(d) $m E^{2}$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 37

The mass and diameter of a planet are twice those of earth. The period of oscillation of pendulum on this planet will be (if it is a second's pendulum on earth)(a) $\frac{1}{\sqrt{2}} \sec$
(b) $2 \sqrt{2} \mathrm{sec}$
(c) $2 \mathrm{sec}$
(d) $\frac{1}{2} \sec$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 38

A spring of force constant $k$ is cut into two pieces such that one pieces is double the length of the other. Then the long piece will have a force constant of
(a) $2 / 3 k$
(b) $3 \angle 2 k$
(c) $3 k$
(d) $6 k$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 39

Two bodies $M$ and $N$ of equal masses are suspended from two separate mass less springs of force constants $k_{1}$ and $k_{2}$ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of $M$ to that of $N$ is
(a) $k_{1} / k_{2}$
(b) $\sqrt{k_{1} / k_{2}}$
(c) $k_{2} / k_{1}$
(d) $\sqrt{k_{2} / k_{1}}$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 40

Two identical springs of constant $k$ are connected in series and parallel as shown in figure. A mass $m$ is suspended from them. The ratio of their frequencies of vertical oscillation will be
(a) $2: 1$
(b) $1: 1$
(c) $1: 2$
(d) $4: 1$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 41

Two identical springs of constant $k$ are connected in series and parallel as shown in figure. A mass $m$ is suspended from them. The ratio of their frequencies of vertical oscillation will be
(a) $2: 1$
(b) $1: 1$
(c) $1: 2$
(d) $4: 1$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 42

A block is placed on a friction less horizontal table. The mass of the block is $m$ and springs of force constant $k_{1}, k_{2}$ are attached on either side with if the block is displaced a little and left to oscillate, then the angular frequency of oscillation will be
(a) $\left(\frac{k_{1}+k_{2}}{m}\right)^{1 / 2}$
(b) $\left[\frac{k_{1} k_{2}}{m\left(k_{1}+k_{2}\right)}\right]^{1 / 2}$
(c) $\left[\frac{k_{1} k_{2}}{\left(k_{1}-k_{2}\right) m}\right]^{1 / 2}$
(d) $\left[\frac{k_{1}^{2}+k_{2}^{2}}{\left(k_{1}+k_{2}\right) m}\right]^{1 / 2}$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 43

A particle of mass $200 \mathrm{gm}$ executes S.H.M. The restoring force is provided by a spring of force constant $80 \mathrm{~N} / \mathrm{m}$. The time period of oscillations is
(a) $0.31 \mathrm{sec}$
(b) $0.15 \mathrm{sec}$
(c) $0.05$ sec
(d) $0.02 \mathrm{sec}$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 44

The length of a spring is $l$ and its force constant is $k$ when a weight $w$ is suspended from it. Its length increases by $x$. if the spring is cut into two equal parts and put in parallel and the same weight $W$ is suspended from them, then the extension will be
(a) $2 x$
(b) $x$
(c) $x / 2$
(d) $x / 4$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 45

A mass $m$ is suspended from a string of length $l$ and force constant $k$. The frequency of vibration of the mass is $f_{1}$. The spring is cut in to two equal parts and the same mass is suspended from one of the parts. The new frequency of vibration of mass is $f_{2}$. Which of the following reaction between the frequencies is correct. [NCERT $198_{3}$; CPMT 1986; MP PMT 1991]
(a) $f_{1}=\sqrt{2} f_{2}$
(b) $f_{1}=f_{2}$
(c) $f_{1}=2 f_{2}$
(d) $f_{2}=\sqrt{2} f_{1}$

RZ

Rubeena Zulfiqar

Numerade Educator