CBSE Questions for Class 11 Engineering Physics Oscillations Quiz 4 - MCQExams.com

Find the length of a simple pendulum such that its time period is $$2\ s$$.
  • $$99.4\ cm$$
  • $$89.4\ cm$$
  • $$79.4\ cm$$
  • $$109.4\ cm$$
A particle performs SHM with a period $$T$$ and amplitude $$a$$. The mean velocity of particle over the time interval during which it travels a distance $$a/2$$ from the extreme position is:
  • $$\dfrac{6a}{T}$$
  • $$\dfrac{2a}{T}$$
  • $$\dfrac{3a}{T}$$
  • None 
The time period of a simple pendulum is 0.2 sec. What is its frequency of oscillation?
  • 0.5 hz
  • 5 Hz
  • 50Hz
  • 1Hz
You are designing a pendulum clock to have a period of $$1.0\ s$$. How long should the pendulum be ?
  • $$0.25\ m$$
  • $$0.50\ m$$
  • $$0.25\ cm$$
  • $$0.25\ mm$$
What is to and fro motion of an object called?
  • Vibratory or oscillatory motion.
  • Rotatory motion
  • Linear motion
  • Curvilinear motion
How does time period (T) of a seconds pendulum vary with length (L) ?
  • $$T\, \propto\, \sqrt L$$
  • $$T\, \propto\, L^2$$
  • $$T\, \propto\, L$$
  • T does not depend on L
A particle moving on x-axis has potential energy $$U=2-20x+5x^{2}$$ Joule along x-axis. The particle is released at $$r=-3$$. The maximum value of $$x$$ will be (x is in meter):
  • $$5\ m$$
  • $$3\ m$$
  • $$7\ m$$
  • $$8\ m$$
A particle performing SHM takes time equal to T (time period of SHM) in consecutive appearances at a particular point. This point is 
  • An extreme position
  • The mean position
  • Between positive extreme and mean position
  • Between negative extreme and mean position
A desktop toy pendulum swings back and forth once every $$1.0 s$$. How long is this pendulum?
  • $$0.25\, m$$
  • $$0.50\, m$$
  • $$0.15\, m$$
  • $$0.30\, m$$
Which of the following is not a necessary apparatus for the measurement of acceleration due to gravity $$(g)$$ by a simple pendulum?
  • Stop watch
  • Screw gauge
  • Spherometer
  • Scale
Given equation of SHM is $$\displaystyle x=10\sin 10\pi t.$$ Find the distance between the two points where speed is $$\displaystyle 50\pi $$ cm/sec; x is in cm and t is in seconds. 
  • $$5(\sqrt 3 +1)$$  cm
  • 20 cm
  • 17.32 cm
  • 8.66 cm
For a particle performing SHM, equation of motion is given as $$\displaystyle \frac{d^{2}x}{dt^{2}}+4x=0$$. Find the time period
  • $$\displaystyle T=\pi $$
  • $$\displaystyle T=2\pi $$
  • $$\displaystyle T=3\pi $$
  • $$\displaystyle T=4\pi $$
The bob of mass $$50   gms$$ of a simple pendulum is replaced by another bob of mass $$75   gms$$. The time period of the simple pendulum
  • Becomes $${75}/{50}$$ times the original period
  • Becomes $${50}/{75}$$ times the original period
  • Becomes $$125$$ times the original period
  • Remains unchanged
The magnitude of acceleration of particle executing SHM at the position of maximum displacement is:
  • zero
  • minimum
  • maximum
  • none of these
A hollow pendulum bob filled with water has a small hole at the bottom through which water escapes at a constant rate. Which of the following statements describes the variation of the time period (T) of the pendulum as the water flows out?
  • T decreases first and then increases.
  • T increases first and then decreases.
  • T increases throughout.
  • T does not change.
The equilibrium position of the particle is
  • x = 4
  • x = 6
  • x = 2
  • x = 3
The bob of a second's pendulum is replaced by another bob of double mass. The new time period will be
  • 4 sec
  • 1 sec
  • 2 sec
  • 3 sec
In the given figure
320683.png
  • The speed of particle B and D are same
  • The speed of particle A, B, E are maximum
  • The particle F has zero speed
  • All particles have same speed
If the period of oscillation of a simple pendulum is 4 second and we want to convert it into a second pendulum, then we have to
  • Make the length of the pendulum one fourth of the previous length
  • Double the length of the pendulum
  • Make the length of the pendulum half of the previous length
  • Double the mass of the bob
The frequency of oscillator of the springs as shown in figure will be
431102.png
  • $$\displaystyle \frac {1}{2\pi} \sqrt {\frac {(k_1+k_2)m}{k_1k_2}}$$
  • $$\displaystyle \frac {1}{2\pi} \sqrt {\frac {k_1k_2}{(k_1+k_2)m}}$$
  • $$\displaystyle \frac {1}{2\pi}\sqrt {\frac {k}{m}}$$
  • $$\displaystyle 2\pi\sqrt {\frac {k}{m}}$$
All oscillatory motions are ______
  • periodic
  • linear
  • rotatory
  • curvilinear
State whether true or false.
The needle of a moving sewing machine executes oscillatory motion.
  • True
  • False
Which is not a necessary assumption for simple pendulum
  • in-extensible, light and flexible string.
  • heavy but small sized sphere (bob).
  • angular displacement from the mean position is very less.
  • volume of the bob is negligible.
Which of the following is an example of motion in one direction?
  • A runner running on a circular track.
  • A bullet fired from a gun.
  • A piece of stone thrown horizontally from a tower.
  • Motion of a wheel.
A pendulum suspended from the ceiling of a train has a time period T when the train is at rest. When the train is accelerating with a uniform acceleration, the time period will
  • increase
  • decrease
  • become infinite
  • remain unaffected
If a pendulum takes $$4 sec$$ to swing in each direction, find the length of the pendulum.
  • 4.2 m
  • 3.97 m
  • 5.2 m
  • 15.9 m
Ratio of kinetic energy at mean position to potential energy at $$A/2$$ of a particle performing SHM.
  • $$2:1$$
  • $$4:1$$
  • $$8:1$$
  • $$1:1$$
A particle is executing simple harmonic motion with an amplitude $$A$$ and time period $$T$$. The displacement of the particles after $$2 T$$ period from its initial position is
  • $$A$$
  • $$4A$$
  • $$8A$$
  • Zero
A simple pendulum performs simple harmonic motion about $$x = 0$$ with an amplitude $$'a'$$ and time period $$'T'$$. The speed of the pendulum at $$x = \dfrac{a}{2}$$ will be:
  • $$\dfrac {\pi a}{T}$$
  • $$\dfrac {3\pi^{2}a}{T}$$
  • $$\dfrac {\pi a\sqrt {3}}{T}$$
  • $$\dfrac {\pi a\sqrt {3}}{2T}$$
Find out the Time period of simple harmonic oscillator vibrating with frequency $$2.5$$ Hz and an amplitude of $$0.05$$m:
  • $$0.4 sec$$
  • $$0.2 sec$$
  • $$8 sec$$
  • $$20 sec$$
  • $$50 sec$$
The displacement time graph of a particle executing S.H.M. is as shown in the figure. The corresponding force-time graph of the particle is:
476990_77e4e484c50d474dbc09f3a968c0fdf6.png

Choose the correct option which describe the simple harmonic motion.

I. The acceleration is constant.

II. The restoring force is proportional to the displacement.

III. The frequency is independent of the amplitude.
  • II only
  • I and II only
  • I and III only
  • II and III only
  • I, II and III
The ratio of the angular speed of minutes hand and hour hand of a watch is:
  • $$6:1$$
  • $$12:1$$
  • $$1:6$$
  • $$1:12$$
The equation of a simple harmonic progressive wave is given by y = A sin (100$$\pi t\, -\, 3x$$). Find the distance between 2 particles having a phase difference of $$\displaystyle \frac {\pi}{3}$$.
  • $$\displaystyle \frac {\pi}{9} m$$
  • $$\displaystyle \frac {\pi}{18} m$$
  • $$\displaystyle \frac {\pi}{6} m$$
  • $$\displaystyle \frac {\pi}{3} m$$
For the block under SHM shown in the figure, which of the following quantities is directly proportional to the maximum speed of the block?

480254.jpg
  • Amplitude
  • Frequency
  • Period
  • Position of block
  • Total mechanical energy of the block
A mass of $$36$$ kg is kept vertically on the top of a massless spring. What is the maximum compression of the spring if the spring constant is $$15000 $$N/m. Assume $$g=10 m/s^2$$.
  • 0.02 m
  • 0.14m
  • 0.0004m
  • 0.2m
  • 42.52m
A block of mass $$m$$ attached to an ideal spring undergoes simple harmonic motion. The acceleration of the block has its maximum magnitude at the point where :
  • the speed is the maximum
  • the potential energy is the minimum
  • the speed is the minimum
  • the restoring force is the minimum
  • the kinetic energy is the maximum
For the block under SHM shown in the figure, which of the following quantities varies sinusoidally with time?

480255.jpg
  • Amplitude
  • Frequency
  • Period
  • Position of block
  • Total mechanical energy of the block
A block of mass $$m=4$$ kg undergoes simple harmonic motion with amplitude $$A=6$$ cm on the frictionless surface. Block is attached to a spring of force constant $$k=400 N/m$$. If the block is at $$x = 6$$ cm at time $$t = 0$$ and equilibrium position is at $$x=0$$ then the blocks position as a function of time (with $$x$$ in centimetres and $$t$$ in seconds)?
  • $$x=6\,sin(10t+\dfrac{1}{2}\pi)$$
  • $$x=6\,sin(10\pi t)$$
  • $$x=6\,sin(10\pi t-\dfrac{1}{2}\pi)$$
  • $$x=6\,sin(10t-\dfrac{1}{4}\pi)$$
Which of the following is true of all systems displaying simple harmonic motion?
  • Movements is always up and down.
  • Movement is always side to side.
  • All SHM systems are man-made.
  • All SHM systems involve springs.
  • For all SHM systems, the amount of force restoring an object to its equilibrium position is proportional to the amount of the object's displacement from equilibrium.
A mass on a frictionless surface is attached to a spring. The spring is compressed from its equilibrium position, B , to point A , a distance x from B . Point C is also a distance x from B, but in the opposite direction. When the mass is released and allowed to oscillated freely, at what point or points is its velocity maximized?
491166.PNG
  • A
  • B
  • C
  • Both A and C
  • Both A and B
The figure above shows the same ideal spring in three different situations.
First without a mass hanging the spring is unstretched.
Next with the blue mass hanging the spring stretches.
Finally with the red mass hanging the spring stretches twice as much as it did with the blue mass.
How much does the red mass weigh compared to the blue mass? 
493296.jpg
  • The red mass weighs twice as much as the blue mass.
  • The red mass weighs four times as much as the blue mass.
  • The red mass weighs half as much as the blue mass.
  • The red mass weighs about 1.4 as much as the blue mass.
  • We cannot determine how much the red mass weighs compared to the blue mass, because we do not know the unstretched length of the spring.
When the mass passes through B, it has
485572.PNG
  • Kinetic energy but no potential energy
  • Potential energy but no kinetic energy
  • Kinetic energy and potential energy
  • No kinetic or potential energy
  • Total energy equal to zero
A block is attached to an ideal spring undergoes simple harmonic oscillations of amplitude A. Maximum speed of block is calculated at the end of the spring. If the block is replaced by one with twice the mass but the amplitude of its oscillations remains the same, then the maximum speed of the block will
  • decrease by a factor of 4
  • decrease by a factor of 2
  • decrease by a factor of $$\sqrt 2$$
  • remain the same
  • increase by a factor of 2
Simple harmonic oscillation of a given system can be specified completely by stating its: 
  • amplitude, frequency and initial phase.
  • amplitude, frequency and wavelength
  • frequency and wavelength.
  • frequency, wavelength and initial phase.
Simple harmonic motion (SHM) is a technical term used to describe a certain kind of idealized oscillation. A simple harmonic oscillation has
  • Fixed frequency and fixed amplitude
  • Fixed frequency and variable amplitude
  • Variable frequency and fixed amplitude
  • Variable frequency and variable amplitude
A spring-mass system oscillates back and forth in positive and negative directions. The graph above shows the acceleration of the mass.
Which of the following graphs best shows the velocity of the mass?
The time axes are scaled the same on all graphs
496491.jpg
Consider a thingy hanging from a spring. The system is set vibrating by pulling the thingy down below its equilibrium position and then letting it go from rest.The frequency of the oscillation is determined by
571740_713f2e8fbe00414c8d595de52cc09de9.png
  • the amount of the initial displacement
  • the mass of the thingy and the properties of the spring
  • the local gravitational field, $$g$$
  • all of the above.
We are still looking at the oscillating thingy hanging from a spring. The system was set vibrating by pulling the thingy down below its equilibrium position and then letting it go from rest. If the initial displacement is doubled what happens to the maximum kinetic energy of the thing?

571780.PNG
  • It is unchanged.
  • It is doubled.
  • It is increased by a factor of 4.
  • We can't tell from the information provided.
When a spring-mass system vibrates with simple harmonic motion, the mass in motion reaches its maximum velocity:
  • when its acceleration is greatest
  • when its acceleration is least.
  • once during one oscillation.
  • when it is as its maximum displacement from equilibrium.
  • when it experiences maximum force.
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