CBSE Questions for Class 11 Engineering Physics Oscillations Quiz 5 - MCQExams.com

A particle executing SHM has a maximum speed of $$0.5 m{s}^{-1}$$ and maximum acceleration of $$1 m {s}^{-2}$$. 
The angular frequency of oscillation is:
  • $$2 rad {s}^{-1}$$
  • $$0.5 rad {s}^{-1}$$
  • $$2\pi rad {s}^{-1}$$
  • $$0.5\pi rad {s}^{-1}$$
The black graph pictured below represents the poition -time graph for a spring -mass system oscillating withnsimple harmonic motion.
The colored, dashed graphs represents shapes of possible velocity time graphs for the same motion.
The vertical axis stands for position or velocity, but the scaling does not matter. The time axis is the same for all graphs.
Which colored graph best represents the possible velocity for the mass in this spring 
493347.jpg
  • red
  • blue
  • green
  • The velocity graph is the same as the position graph
  • All three colored graphs are equally possible.
The black graph pictured above represents the position-time graph for a spring-mass system oscillating with simple harmonic motion.
The colored, dashed graphs represent shapes of possible velocity time graphs for the same motion.
The vertical axis stands for position or velocity, but the scaling does not matter. The time axis is the same for all graphs.
Which colored graph best represents the possible velocity for the mass in this spring-mass system?
496476.jpg
  • Red
  • Blue
  • Green
  • The velocity graph is the same as the position graph
  • All three colored graphs are equally possible
In their discussions of SHM text books sometimes consider a thingy attached to a horizontal spring and moving horizontally on a frictionless surface, instead of the hanging thingy that we have been looking at. Suppose that the two springs and the two thingies are identical. Think about whether these two systems are significantly different in other respects and decide which one of the following statements is true.
571794.PNG
  • The systems have different periods because their motions are aligned differently with the gravitational field.
  • The hanging system has a slightly smaller period because the weight of the spring has to be accounted for.
  • The hanging system has a slightly larger period because the weight of the spring has to be accounted for.
  • The two systems have identical periods, no matter what the weight of the spring is.
Which of  the  following regarding oscillatory motion is true?
  • Motion of the earth is periodic but not oscillatory because it is not to and fro.
  • Quivering of the string of the musical instrument is an example of oscillatory motion
  • Motion of the earth is periodic and oscillatory motion because it is not to and fro.
  • None of the above
Which of the following is an example of oscillatory motion? 
  • Heart beat of a persion
  • Motion of earth around the sun
  • Motion of Hally's comet around the sun
  • Oscillations of a simple pendulam
An object swinging on the end of a string forms a simple pendulum. Some students (and some texts) often cite the simple pendulum's motion as an example of SHM. That is not quite accurate because the motion is really
  • approximately SHM only for small amplitudes
  • exactly SHM only for amplitudes that are smaller than a certain value
  • approximately SHM for all amplitudes.
  • None of the above
Simple harmonic motion (SHM) is a technical term used to describe a certain kind of idealized oscillation. Practically all the oscillations that one can see directly in the natural world are much more complicated than SHM. Why then do physicists make such a big deal out of studying SHM?
  • It is the only kind of oscillation that can be described mathematically
  • Any real oscillation can be analysed as a superposition (sum or integral) of SHMs with different frequencies
  • Physics is concerned mainly with the unnatural world.
  • Students are too stupid to appreciate the real world.
Which of the following conditions must be satisfied for a body to oscillate or vibrate?
A: The body must have inertia to keep it moving across the mid point of its path.
B: There must be a restoring force to accelerate the body towards the midpoint.
C: The fractional force acting on the body against its motion must be small.
  • Only A
  • Only A and B
  • Only B and C
  • All A, B and C
The velocity  vector $$v$$ and displacement vector $$x$$ of a particle executing SHM are related as $$\dfrac{v dv}{dx} ={\omega}^2 x$$ with the initial condition $$v = v_0$$ at  $$x = 0$$. The velocity $$v$$, when displacement is $$x$$, is:
  • $$v = \sqrt{v^2_0 + {\omega}^2x^2}$$
  • $$v = \sqrt{v^2_0 - {\omega}^2x^2}$$
  • $$v = {3}\sqrt{v^3_0 + {\omega}^3x^3}$$
  • $$v = v_0 - ({\omega}^3 x^3 e^{x^3})^{1/3}$$
The displacement of a particle is represented by the equation $$y=3 cos(\dfrac{\pi}{4}- 2 \omega t)$$. The motion of the particle is :
  • simple harmonic with period $$\dfrac{2 \pi}{\omega}$$
  • simple harmonic with period $$\dfrac{ \pi}{\omega}$$
  • periodic but not simple harmonic
  • non-periodic.
A particle vibrating simple harmonically has an acceleration of $$16{cms}^{-2}$$ when it is at a distance of $$4cm$$ from the mean position. Its time period is
  • $$1s$$
  • $$2.572s$$
  • $$3.142s$$
  • $$6.028s$$
The amplitude of an oscillating simple pendulum is 10 cm and its time period is 4s. Its speed after is when it passes through its equilibrium position is :
  • Zero
  • 2.0 m/s
  • 0.3 m/s
  • 0.4 m/s
A mass of 2.0 kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released the mass executes a simple harmonic motion. The spring constant is 200 N/m. What should be the minimum amplitude of the motion, so that the mass gets detached from the pan?
(Take $$\displaystyle g=10{ m }/{ { s }^{ 2 } }$$)
662066_2c40e0dea0bd4a59854c0403b26c827d.JPG
  • 8.0 cm
  • 10.0 cm
  • Any values less than 12.0 cm
  • 4.0 cm
Identify the wrong statement from the following:
  • If the length of a spring is halved, the time period of each part becomes $$\frac {1}{\sqrt{2}}$$ times the original
  • The effective spring constant K of springs in parallel Is given by $$\frac {1}{K}=\frac {1}{K_1}+\frac {1}{K_2}+ ....$$
  • The time period of a stiffer spring is less than that of a soft spring
  • The spring constant is inversely proportional to the spring length
  • The unit of spring constant is $$Nm^{-1} $$
A particle moves so that its acceleration a is given by $$a = bn$$, where x is displacement from equilibrium position and b is non negative real constant. The time period of oscillation of the particle is :
  • $$2 \pi \sqrt{b}$$
  • $$\dfrac{2 \pi}{\sqrt{b}}$$
  • $$\dfrac{2\pi}{b}$$
  • $$2 \sqrt{\dfrac{\pi}{b}}$$
The simple harmonic motion of a particle is given by $$x=a\sin 2\pi t$$. Then, the location of the particle from its mean position at a time $$1/8$$th of a second is:
  • $$a$$
  • $$\displaystyle\frac{a}{2}$$
  • $$\displaystyle\frac{a}{\sqrt{2}}$$
  • $$\displaystyle\frac{a}{4}$$
  • $$\displaystyle\frac{a}{8}$$
A spring with force constant $$k$$ is initially stretched by $$x_{1}$$. If it further stretched by $$x_{2}$$, then the increase in its potential energy is
  • $$\dfrac {1}{2}k(x_{2} - x_{1})^{2}$$
  • $$\dfrac {1}{2}kx_{2}(x_{2} + 2x_{1})$$
  • $$\dfrac {1}{2}\ kx_{1}^{2} + \dfrac {1}{2}\ kx_{2}^{2}$$
  • $$\dfrac {1}{2}\ k(x_{1} + x_{2})^{2}$$
  • $$\dfrac {1}{2}\ k(x_{1} + x_{2})^{3}$$
For a simple pendulum, relation between time period $$T$$, length of pendulum $$l$$ and acceleration due to gravity $$g$$ is given by : 
  • $$T=2 \pi \dfrac{l}{\sqrt{g}}$$
  • $$T=2 \pi \sqrt{\dfrac{l}{g}} $$
  • $$T=2 \pi \dfrac{l}{g}$$
  • None of these
A particle which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance $$x$$ of the particle from the origin is $$F(x)=-kx+a{ x }^{ 3 }$$. Here, $$k$$ and $$a$$ are positive constants. For $$x\ge 0$$, the functional form of the potential energy $${U}_{(x)}$$ of the particle is :
 If the differential equation for a simple harmonic motion is  $$\dfrac {d^2y}{dt^2} +2y= 0$$, the time period of the motion is 
  • $$\pi \sqrt{2} s$$
  • $$\dfrac {\sqrt{2}} {\pi} s$$
  • $$\dfrac {\pi}{\sqrt{2}} s$$
  • $$2 \pi s$$
  • $$\dfrac {\sqrt{\pi}} {2} s$$
When a simple pendulum is taken from the Equator to the Pole, its period of oscillation will :
  • increase
  • decrease
  • remains same
  • can't say
Which one of the following is simple harmonic?
  • Rotation of earth around the sun
  • Rotation of earth about its own axis
  • Revolving motion of a top
  • Motion of a steel ball in a viscous medium
  • Motion of oscillating liquid column in U-tube
The amplitude and the periodic time of a SHM are $$5cm$$ and $$6s$$ respectively. At a distance of $$2.5cm$$ away from the mean position, the phase will be
  • $$\cfrac { \pi }{ 3 } $$
  • $$\cfrac { \pi }{ 4 } $$
  • $$\cfrac { \pi }{ 6 } $$
  • $$\cfrac { 5\pi }{ 12 } \quad $$
A 2 kg block is dropped from a height $$ 0.4 m $$ on a spring of force constant $$k=1960 N/m$$.The maximum compression of spring is 
  • $$ 0.1 m$$
  • $$ 0.2 m$$
  • $$ 0.3 m$$
  • $$ 0.4 m$$
Four springs having the same force constant and a mass $$M$$ are connected between rigid walls as shown in figure. The system with smallest time period is
The displacement of a particle in SHM is $$x=10\sin \begin{pmatrix}2t-\dfrac{\pi}{6}\end{pmatrix}m.$$ When its displacement is 6 m, the velocity of the particle (in $$ms^{-1}$$) is
  • 8
  • 24
  • 16
  • 10
  • 12
The motion of a particle executing SHM in one dimension is described by $$x=-0.3 \, sin \, \left ( t+\frac {\pi}{4} \right )$$  where, x is in metre and t in second. The frequency of oscillation in Hz is
  • $$3$$
  • $$\dfrac {1}{2\pi}$$
  • $$\dfrac {\pi}{2}$$
  • $$\dfrac {1}{\pi}$$
Which one of the following represents simple harmonic motion ?
  • $$x^{2}=a+bv$$
  • $$x=\sqrt{a+bv^{2}}$$
  • $$x=a-bv$$
  • $$x=\sqrt{a-bv^{2}}$$
Velocity at mean position of a particle executing SHM is v, then velocity of the particle at a distance equal to half of the amplitude is
  • $$\frac {\sqrt{3}}{2}v$$
  • $$\frac {2} {\sqrt{3}}v$$
  • $$2v$$
  • $$v$$
The average total energy in one time period of a particle of mass $$m$$ executing SHM of amplitude $$a$$ and angular velocity $$\omega $$ is
  • $$\dfrac { 1 }{ 2 } m{ \omega }^{ 2 }{ a }^{ 2 }$$
  • $$\dfrac { 1 }{ 4 } m{ \omega }^{ 2 }{ a }^{ 2 }$$
  • $$0$$
  • $$m{ \omega }^{ 2 }{ a }^{ 2 }$$
  • $$\dfrac { 1 }{ 8 } m{ \omega }^{ 2 }{ a }^{ 2 }$$
A tunnel is dug along the diameter of the earth. A mass $$m$$ is dropped into it. How much time does it take to cross the earth?
  • $$169.2\ minutes$$
  • $$84.6\ minutes$$
  • $$21.2\ minutes$$
  • $$42.3\ minutes$$
One end of a rod of length L is fixed to a point on the circumference of a wheel of radius R. The other end is sliding freely along a straight channel passing through the centre O of the wheel as shown in the figure. The wheel is rotating with a constant angular velocity $$\omega$$ about O. Taking $$\displaystyle T=\frac{2\pi}{P\omega}$$ the motion of the rod is?
739636_2e9709c86a8549aa8e236b279528d300.png
  • Simple harmonic with a period of T
  • Simple harmonic with a period of $$T/2$$
  • Not simple harmonic but periodic with a period of T
  • Not simple harmonic but periodic with a period of $$T/2$$
A pendulum swings backwards and forwards passing through Y, middle point of the oscillation. The first time of pendulum passes through Y, a stopwatch is started. The twenty-first time the pendulum pass through Y, the stopwatch is stopped. The reading is T.
What is the time period of pendulum? 
809613_a9bed2f166d245df8c9e6b150ae39d8c.png
  • T/40
  • T/21
  • T/20
  • T/10
The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and $${E}_{1}$$ and $${E}_{2}$$ are the total mechanical energies respectively. Then
784516_37026cf67edc423fb0f7d1c52c806026.png
  • $${ E }_{ 1 }=\sqrt { 2 } { E }_{ 2 }$$
  • $${ E }_{ 1 }=2{ E }_{ 2 }$$
  • $${ E }_{ 1 }=4{ E }_{ 2 }$$
  • $${ E }_{ 1 }=16{ E }_{ 2 }$$
A particle performing S.H.M. having amplitude 'a' possesses velocity $$\dfrac {(3)^{1/2}}{2}$$ times the velocity at the mean position. The displacement of the particle shall be
  • $$a/2$$
  • $$(3)^{1/2}\frac{a}{2}$$
  • $$(\dfrac {a}{ {2}})^{1/2}$$
  • $$(2)^{1/2}a$$
An oscillator consists of a block attached to a spring (k = 400 N/m). At some time t, the position (measured from the system's equilibrium location), velocity and acceleration of the block are x = 0.100m, v = 13.6 m/s, and a = 123 m/s$$^2$$. The amplitude of the motion and the mass of the block are
  • $$0.2 m, 0.845 kg$$
  • $$0.3 m, 0.765 kg$$
  • $$0.4 m, 0.325 kg$$
  • $$0.5 m, 0.445 kg$$
A particle performs S.H.M of amplitude $$A$$ along a straight line. When it is at distance $$\cfrac { \sqrt { 3 }  }{ 2 } A$$ from mean position, its kinetic energy gets increased by an amount $$\cfrac { 1 }{ 2 } m{ \omega  }^{ 2 }{ A }^{ 2 }$$ due to an impulsive force. Then its new amplitude becomes
  • $$\cfrac { \sqrt { 5 } }{ 2 } A$$
  • $$\cfrac { \sqrt { 3 } }{ 2 } A$$
  • $$\sqrt { 2 } A$$
  • $$\sqrt { 5 } A$$
An oscillator is producing FM waves of frequency 2kHz with avariation of 10kHz. The modulating index=?
  • 0.20
  • 5.0
  • 0.67
  • 1.5
Three masses of $$500g,300g$$ and $$100g$$ are suspended at the end of a spring as shown and are in equilibrium. When the $$500g$$ mass is removed suddenly, the system oscillates with a period of $$2$$ second. When the $$300g$$ mass is also removed, it will oscillate with a period
874198_43058ee2f7c8405bad802faa5745ecc8.png
  • $$2$$ sec
  • $$4$$ sec
  • $$8$$ sec
  • $$1$$ sec
Uniform circular motion can also be represented by a simple harmonic oscillator.
State whether given statement is True/False?
  • True
  • False
In an electronic watch, the component corresponding to the pendulum of a pendulum clock is a__?
  • Diode
  • Transistor
  • Crystal oscillator
  • Balance wheel
In case of a simple harmonic motion, if the velocity is plotted along the X-axis and the displacement (from the equilibrium position)(is plotted along the Y-axis, the resultant curve happens to be an ellipse with the ratio:
$$\displaystyle\frac{major axis(along X)}{minor axis (along Y)}=20\pi$$
What is the frequency of the simple harmonic motion?
  • $$100$$Hz
  • $$20$$Hz
  • $$10$$Hz
  • $$\displaystyle\frac{1}{10}$$Hz
Which one of the following will take place when a watch based on oscillating spring is taken to a deep mine?
  • It will indicate the same time  on earth
  • It will become fast
  • It will become slow
  • It will stop working
A particle executing simple harmonic motion with time period T. The time period with which its kinetic energy oscillates is
  • T
  • $$2$$T
  • $$4$$T
  • $$\frac{T}{2}$$
The time period of simple harmonic motion depends upon the
  • amplitude.
  • energy
  • phase constant
  • mass
The displacement of a particle varies with time according to the relation $$y = a sin \omega t + b cos \omega t.$$
  • The motion is oscillatory but not SHM.
  • The motion is SHM with amplitude a + b.
  • The motion is SHM with amplitude $$a^2 + b^2$$
  • The motion is SHM with amplitude $$\sqrt{a^2 + b^2}$$
A block of mass $$m$$ is hanging vertically by spring of spring constant $$k$$. If the mass is made to oscillate vertically, its total energy is:
  • Maximum at the extreme position
  • Maximum at the mean position
  • Minimum at the mean position
  • Same at all positions
A particle executing simple harmonic motion with an amplitude $$5$$ cm and a time period $$0.2$$s. The velocity and acceleration of the particle when the displacement is $$5$$ cm is
  • $$0.5 \pi m s^{-1}, 0 m s^{-2}$$
  • $$0.5 m s^{-1}, -5 \pi^2 m s^{-2}$$
  • $$0 m s^{-1}, -5 \pi^2 m s^{-2}$$
  • $$0.5\pi m s^{-1}, -0.5 \pi^2 m s^{-2}$$
Match the Column I with Column II
938540_5d7f56a930df482fbc9752ba221ff440.jpg
  • A - p, B - q, C - s. D - r
  • A - s, B - r, C - p, D - q
  • A - r, B - p, C - s. D - q
  • A - p, B - r, C - q, D - s
0:0:1


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