CBSE Questions for Class 11 Engineering Physics Oscillations Quiz 14 - MCQExams.com

Two particles are executing simple harmonic motion of the same amplitude $$A$$ and frequency $$\omega$$ along the x-axis. Their mean position is separated by distance $${X}_{0}({X}_{0}> A)$$. If the maximum separation between them is $$({X}_{0}+A)$$, the phase difference between their motion is 
  • $$\pi /2$$
  • $$\pi /3$$
  • $$\pi /4$$
  • $$\pi /6$$
Three measurements of the time for $$20$$ oscillations of a pendulum give $$t_1 = 39.6_s , t_2 = 39.9_s and t_3 = 39.5_s$$. The precision in the measurement, is  
  • $$0.005 sec$$
  • $$0.01 sec$$
  • $$1 sec$$
  • $$2 sec$$
A particle of mass 0.1 kg executes SHM under a force F= (-10x)N. Speed of particle at mean position is 6 m/s. Then amplitude of oscillations is
  • 0.6 m
  • 0.2 m
  • 0.4 m
  • 0.1 m
In the arrangement shown, the solid cylinder of mass m is slightly rolled to the left and released. It starts oscillating on the horizontal surface without slipping. Then time period of oscillation is 
1255169_1fb487eac73348c2803a6a8b9ecb16aa.png
  • $$\pi \sqrt { \dfrac { 3K }{ m } } $$
  • $$2\pi \sqrt { \dfrac { 3M }{ 2K } } $$
  • $$2\pi \sqrt { \dfrac { 2K }{ 3M } } $$
  • $$2\pi \sqrt { \dfrac { 3K }{ 2m } } $$
A bob is suspended with the help of a light and rigid rod of length l. A spring of spring consatnt k is also attached. what should be the value of I so the period for small oscillation is $$ \pi \sqrt \frac { I } { g } $$
1249787_887549fd6e8a48e1becb16d8b6b4503c.png
  • $$ \frac { mg } { k } $$
  • $$ \frac { 2mg } { k } $$
  • $$ \frac { 3mg } { k } $$
  • $$ \frac { 4mg } { k } $$
If $$y= \sin^2\omega t$$ represents the displacement of a particle performing SHM, the particle oscillates between 
  • $$-1$$ and $$-\frac { 1} {2}$$
  • $$-\frac {1} {2}$$ and $$-\frac {1} {2}$$
  • $$-1$$ and $$0$$
  • $$0$$ and $$+1$$
A particle moves on the $$X-$$ axis according to the equation $$x=x_0\sin^{2}\omega t$$. The motion is simple harmonic 
  • With amplitude $$x_0$$
  • With amplitude $$2\ x_0$$
  • With time period $$\dfrac {2\pi}{\omega}$$
  • With time period $$\dfrac {\pi}{\omega}$$.
Two particles are in $$SHM$$ with same amplitude $$A$$ and same angular frequency $$\omega$$. At time $$t=0$$, one is at $$x=+\dfrac{A}{2}$$ and other is at $$x=-\dfrac{A}{2}$$. Both are moving in same direction.
  • Phase difference between the two particle is $$\dfrac{\pi}{3}$$
  • Phase difference between the two particle is $$\dfrac{2\pi}{3}$$
  • They will collide after time $$t=\dfrac{\pi}{2\omega}$$
  • They will collide after time $$t=\dfrac{3\pi}{\omega}$$
Maximum tension to the minimum tension in the string during oscillations is?(Consider amplitude of oscillation =$$ \theta $$)
  • $$(1+\theta^2):(1-\theta^2)$$
  • $$(1+\theta^2):(1-\dfrac{\theta^2}{2})$$
  • $$(1+\theta^2):1$$
  • $$(1+\dfrac{\theta^2}{2}):(1-\theta^2)$$
A  particle executes SHM  along the line AB . IFC divided AB in the ratio 3 : 1, the ration of the time taken to travel AC and CB is : 
  • 3:1
  • 1:1
  • 2:1
  • 4:1
The period of a conical pendulum of string length $$\sqrt 2$$ is $$2 \ s$$. The radius of the bob's orbit is about horizontal is $$[g=9.8 \ m/s^2]$$
  • $$\cfrac 1{\sqrt 2} \ m$$
  • $$1 \ m$$
  • $$\sqrt 2 \ m$$
  • $$\sqrt 3 \ m$$
A SHM is given by$$y = 2(sin \omega t + cos \omega t)$$. Which of the following statements are true-
  • The amplitude is 1 m
  • The amplitude is $$2 \sqrt 2m$$
  • When t = 0, the amplitude is 0 m
  • When t = 0, the amplitude is 2 m
A particle executing SHM while moving from one extreme is found at distance $$x_1,\, x_2$$ and $$x_3$$ from the centre at the end of three successive seconds. The time period of oscillation is: Here  $$\theta  = {\cos ^{ - 1}}\left( {\frac{{{x_1} + {x_3}}}{{2{x_2}}}} \right)$$
  • $$\dfrac {2 \pi}{\theta}$$
  • $$\dfrac { \pi}{\theta}$$
  • $$\theta$$
  • $$\dfrac { \pi}{2\theta}$$
A block of mass $$M$$ is performing $$SHM$$ with amplitude $$A$$ on a smooth horizontal surface$$.$$ At the extreme position a small block of mass $$m$$ falls vertically and sticks to$$M.$$ then$$,$$ amplitude of oscillation will be                                               
  • $$A$$
  • $$A\sqrt {\dfrac{M}{{M + m}}} $$
  • $$A\left( {\dfrac{M}{{M + m}}} \right)$$
  • $$A\left( {\dfrac{{M + m}}{m}} \right)$$
A particle of mass $$m$$ is allowed to oscillate on a smooth parabola: $${ x }^{ 2 }=4ay,a>1$$ as shown in the  figure. The angular frequency $$\left( \omega  \right) $$ of small oscillations is 
 
1303958_d8b82bbcff9a42bd9a02858884004ab2.png
  • $$\omega =\sqrt { \dfrac { g }{ 4a } } $$
  • $$\omega =\sqrt { \dfrac { g }{ 2a } } $$
  • $$\omega =\sqrt { \dfrac { 2g }{ a } } $$
  • $$\omega =\sqrt { \dfrac { g }{ a } } $$
If two wires of same length $$\ell $$ and area of cross section A with young modulus y and 2y connect in series and one end is fixed on roof and other end with mass m. Make simple harmonic motion, then the time period is-
  • $$2\pi \sqrt { \dfrac { m\ell }{ YA } } $$
  • $$2\pi \sqrt { \dfrac { m\ell }{ 3YA } } $$
  • $$2\pi \sqrt { \dfrac { 3m\ell }{ 2YA } } $$
  • $$2\pi \sqrt { \dfrac { m\ell }{ 2YA } } $$

A linear harmonic oscillator of force constant $$6 \times 10^5 N/m$$ and amplitude $$4 $$ cm, has total energy $$600 J$$. Select the correct statement.
  • Maximum potential energy is $$600$$ J
  • Maximum kinetic energy is $$480$$ J
  • Minimum potential energy is $$120$$ J
  • None
A particle executing S.H.M. given by equation $$ y= 8 sin 6 \pi t $$ is sending out waves in a continuous medium traveling at 200 cm/s. the resultant displacement of the particle 150 cm, from B and one second after commencement of vibration of B is:
  • 4 cm
  • 8 cm
  • -8 cm
  • -3 cm
Equation of SHM is x = 10 sin 10 $$\pi t$$. Find the distance between the two points where speed is $$50\pi$$ m/s. x is in cm and t is in seconds. 
  • 10 cm
  • 14 cm
  • 17.32 cm
  • 8.66 cm
A simple pendulum of length 1 m is oscillating with an angular frequency 10 rad/s. The support of the pendulum starts oscillating up and down with a small angular frequency off 1 rad/s and an amplitude of $${ 10 }^{ -2 }.$$ The relative change in the angular frequency of the pendulum is best given by:
  • $${ 10 }^{ -5 }rad/s$$
  • $${ 10 }^{ -1 }rad/s$$
  • $${ 10 }^{ }rad/s$$
  • $${ 10 }^{ -3 }rad/s$$
As shown in figure a horizontal platform with a mass $$m$$ placed on it is executing SHM along y-axis. If the amplitude of oscillation is $$2.5cm$$, the minimum period of the motion for the mass not to be detached from the platform is 
($$g=10m/{sec}^{2}={\pi}^{2}$$)
1324716_73b6e22c284e4df999afc2f3e075c04b.png
  • $$\cfrac{10}{\pi}s$$
  • $$\cfrac{\pi}{10}s$$
  • $$\cfrac{\pi}{\sqrt{10}}s$$
  • $$\cfrac{1}{\sqrt{10}}s$$
Two particles are in SHM in a straight line about same equilibrium position. Amplitude $$A$$ and time period $$T$$ of both the particles are equal. At time $$t = 0$$, one particle is at displacement $$y_{1} = +A$$ and the other at $$y_{2} = -A/2$$, and they are approaching towards towards each other. After what time they cross each other?
  • $$T/3$$
  • $$T/4$$
  • $$5T/6$$
  • $$T/6$$
A thin hoop of radius r and mass m is suspended from a rough rod as shown. Determine the time period of small oscillaion of the hoop in a direction perpendicular to the plane of the hoop. Assume that friction is sufficiently large to prevent slipping at A.
1340098_549e93d1a04a4afca3a3b78786d78a0e.png
  • $$2 \pi \sqrt {\cfrac g R}$$
  • $$2 \pi \sqrt {\cfrac {3R} {2g}}$$
  • $$2 \pi \sqrt {\cfrac R {2g}}$$
  • None
A horizontal plank has a rectangular block placed on it. The plank starts oscillating vertically and simple harmonically with an amplitude of $$40\ cm$$. The block just loses contact with the plank when the latter is at momentary rest. Then
  • the period of oscillation is $$\left( \dfrac { 2\pi }{ 5 } \right) $$
  • the block weight double its weight, when the plank is at one of the position of momentary rest
  • the block weighs 0.5 times its weight on the plank halfway up
  • the block weighs 1.5 times its weight on the plank halfway down.
$$ABC$$ is an equilateral triangle structure up of a light rigid material. Find the frequency of small vertical oscillations of mass $$m$$ along $$AG$$. Conisider $${k}_{1}={k}_{2}={k}_{3}={k}_{4}=k$$
1321182_1c31d5468dbb4b46a27c1a8d4b7fcc21.PNG
  • $$\sqrt{\cfrac{5k}{2m}}$$
  • $$\sqrt{\cfrac{4k}{m}}$$
  • $$\sqrt{\cfrac{3k}{5m}}$$
  • $$\sqrt{\cfrac{10k}{9m}}$$
The length of simple pendulum is about 100 cm known to have an accuracy of 1 mm. Its period of oscillation is 2 s determined by measuring the time for 100 oscillations using a block of 0.1 s resolution. What is the accuracy in the determined value g?
  • 0.2%
  • 0.5%
  • 0.1%
  • 2%
A spring is placed in vertical position by suspending it from a hook at its top. A similar hook on the bottom of the spring is at $$11\ cm$$ above a table top. A mass of $$75\ g$$ and of negligible size is then suspended from the bottom hook, which is measured to be $$4.5\ cm$$ above the table top. The mass is then pulled down a distance of $$4\ cm$$ and released. Find the approximate position of the bottom hook after $$s$$?
Take $$g=10m/{s}^{2}$$ and hooks mass to be negligible.
  • $$5cm$$ above the table top
  • $$4.5cm$$ above the table top
  • $$9cm$$ above the table top
  • $$0.5cm$$ above the table top
A particle executes simple harmonic motion and is located at $$x = a, b$$ and $$c$$ at times $$t_{0}, 2t_{0}$$ and $$3t_{0}$$ respectively. The frequency of the oscillation is
  • $$\dfrac {1}{2\pi t_{0}}\cos^{-1} \left (\dfrac {a + c}{2b}\right )$$
  • $$\dfrac {1}{2\pi t_{0}}\cos^{-1} \left (\dfrac {a + b}{2c}\right )$$
  • $$\dfrac {1}{2\pi t_{0}}\cos^{-1} \left (\dfrac {2a + 3c}{2b}\right )$$
  • $$\dfrac {1}{2\pi t_{0}}\cos^{-1} \left (\dfrac {a + 2b}{3c}\right )$$
A $$1.8$$ g mass suspended by a spring with a spring constant of $$3$$ N/m is forced to oscillate in viscous medium (b=$$2$$ g/s) by a driving force of F=$${10^{ - 3}}$$ sin$$40$$t (in SI units). the amplitude of the driven oscillations will be
  • $$3.4 \times {10^{ - 6}}{m^2}$$
  • $$3.6 \times {10^{ 5}}{m^2}$$
  • $$3.4 \times {10^{ 3}}{m^2}$$
  • $$2.4 \times {10^{ 2}}{m^2}$$
If a body of mass 0.98 kg is made to oscillate on a spring of force constant 4.84 N/m, the angular frequency of the body is
  • 1.22 rad/s
  • 2.22 rad/s
  • 3.22 rad/s
  • 4.22 rad/s
The time period of particle performing linear SHM is 12 s what is time taken by it to cover distance equal to half its amplitude starting its motion from the mean position?
  • 1sec
  • 2sec
  • 3sec
  • 4sec
If the maximum speed of a particle in SHM is $$5\ m/s$$. The average speed of the particle is SHM is equal to
  • $$\dfrac {5}{\pi}m/s$$
  • $$\dfrac {10}{\pi}m/s$$
  • $$\dfrac {5}{2}m/s$$
  • Zero
Frequency $$f$$ of a simple pendulum depends on its length $$\ell$$ and acceleration $$g$$ due to gravity according to the following equation $$f=\dfrac{1}{2\pi}\sqrt{\dfrac{g}{l}}$$. Graph between which of the following quantities is a straight line ?
  • $$f$$ on the ordinate and $$\ell$$ on the abcissa
  • $$f$$ on the ordinate and $$\sqrt{\ell}$$ on the abcissa
  • $$f^{2}$$ on the ordinate and $$\ell$$ on the abcissa
  • $$f^{2}$$ on the ordinate and $$1/\ell$$ on the abcissa
A particle is executing SHM with time period T.Starting from mean position, time taken by it to complete $$cfrac 5 8$$ oscillations, is 
  • $$\cfrac T {12}$$
  • $$\cfrac T {6}$$
  • $$\cfrac {5T} {12}$$
  • $$\cfrac {7T} {12}$$
If velocity of a particle in SHM at x=4 m and x=5 m are 15 m/s and 13 m/s then its time period will be:
  • $$ \pi $$ /4
  • $$ \pi $$ /2
  • $$ \pi $$
  • 4$$ \pi $$ /5
The motion represented by equation $$x=2\sin \omega t+3\sin^{2}\omega t$$ is
  • Periodic
  • Oscillatory
  • $$SHM$$
  • Both (1) & (2)
In a simple oscillating pendulum, the work done by the string in one oscillation will be 
  • Equal to the total energy of the pendulum
  • Equal to the $$K.E$$ of the pendulum
  • Equal to the $$P.E$$ of the pendulum
  • Zero
An iron ball of mass $$M$$ is hanged from the ceiling by a spring with a spring constant $$k$$. It executes a $$SHM$$ with a period $$P$$. If the mass of the ball is increased by four times, the new  period will be 
  • $$4\ P$$
  • $$\dfrac{P}{4}$$
  • $$2\ P$$
  • $$P$$
Initially  mass m is held such that spring is in relaxed condition . if mass m is suddenly released maximum elongation in spring will be 
1390148_f1ca0b0643c845bab9a03fbc22906534.PNG
  • $$ \dfrac {mg}{k} $$
  • $$ \dfrac {2mg}{k} $$
  • $$ \dfrac {mg}{2k} $$
  • $$ \dfrac {mg}{4k} $$
Aa particle executes simple harmonic motion with a speed of $$T\ s$$ and magnitude $$A\ m$$. The shortest time it takes to reach a point $$\dfrac{A}{\sqrt{2}}\ m$$ from its mean position in seconds is:
  • $$T$$
  • $$T/4$$
  • $$T/8$$
  • $$T/16$$
A pendulum bob of weight IN is beld at an angle $$\theta$$ from the vertical by a horizontal force of 2$$N$$ ashown. The tension in the string supporting the pendulum bob (in newton) is 
  • $$\frac { 1 } { \cos \theta }$$
  • $$\frac { 2 } { 2 \sin \theta }$$
  • $$\sqrt { 15 }$$
  • 1
A pendulum clock keeps correct time at $$20^{o}C$$. The correction to be made during summer per day, when the average temperature is $$40^{o}C, (\alpha =10^{-5}/^{o}C)$$  will be:
  • $$5.64\ sec$$
  • $$6.64\ sec$$
  • $$7.64\ sec$$
  • $$8.64\ sec$$
Two pendulums have time periods $$T$$ and 5$$T / 4 .$$ They start SHM at the same time from the mean position. After how many oscillations of the smaller pendulum they will be again in the same phase:
  • $$5$$
  • $$4$$
  • $$11$$
  • $$9$$
A particle executes simple harmonic motion of time period T. At t=0, it is at rest and moves towards positive amplitude then :-
  • Particle initial phase will be $${ 0 }^{ \circ }$$
  • Particle velocity will be zero after T/2 time interval.
  • Particle's velocity becomes half of the maximum velocity first time after T/12.
  • Particle initial phase will be $$\left( -\dfrac { \pi }{ 2 } \right) $$
A block of mass m moving with speed v compresses a spring through distance X before its speed is halved.What is the value of spring constant?
  • $$\dfrac{{3m{v^2}}}{{4{x^2}}}$$
  • $$\dfrac{{m{v^2}}}{{4{x^2}}}$$
  • $$\dfrac{{m{v^2}}}{{2{x^2}}}$$
  • $$\dfrac{{2m{v^2}}}{{{x^2}}}$$
Two particles $$P$$ and $$Q$$ describe $$S.H.M.$$ of same amplitude $$a$$, same frequency $$f$$ (this is not angular frequency $$\omega=\dfrac{2\pi}{T}$$ but it is $$f=\dfrac{1}{T}$$) along the same straight line. The maximum distance between two particles is $$a\sqrt{2}$$. The phase difference between the particles is:
  • $$Zero$$
  • $$\pi/2$$
  • $$\pi/6$$
  • $$\pi/3$$
A pendulum of mass  $$1{ kg }$$  and length  $$l = 1  { m }$$  is released from rest at angle  $$\theta = 60 ^ { \circ }.$$  The power delivered by all the forces acting on the bob at angle  $$\theta = 60 ^ { \circ }$$  will be  $$\left(  { g } = 10  { m } / { s } ^ { 2 } \right).$$ 
  • $$13.4 W$$
  • $$20.4 W$$
  • $$26.6 W$$
  • zero
Which of the following expressions does not represent Simple Harmonic Motion?
  • $$A \cos \omega t$$
  • $$A \sin \omega t$$
  • $$A \sin \omega t+B \cos \omega t$$
  • $$Ae^{\sin \omega\ t}$$
A bullet of mass 10 g moving horizontally with a velocity of $4 400 ms^{-1} $$ strikes a wood block of mass 2 kg which is suspended by light inextensible string of length 5 m. as a result, the centre of gravity of the block found to rise a vertical distance of 10 cm . the speed of the bullet after it emerges out horizontally from the block will be 
  • $$ 100 ms^{-1} $$
  • $$ 80 ms^{-1} $$
  • $$ 120 ms^{-1} $$
  • $$ 160 ms^{-1} $$
Two blocks of masses $$m_{1}=m$$ and $$m_{2}3\ m$$ are connected by a spring of force constant $$k$$ and placed on a horizontal frictionless surface as shown in the fig. The spring is stretched by an amount $$x$$ and released. The system executes simple harmonic motion. The relative velocity of the blocks when the spring is at its natural length is 
  • $$x \sqrt{\dfrac{3\ k}{2\ m}}$$
  • $$2x \sqrt{\dfrac{k}{m}}$$
  • $$\dfrac{x}{2} \sqrt{\dfrac{k}{2\ m}}$$
  • $$2x \sqrt{\dfrac{k}{3\ m}}$$
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