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Oscillations
Q 1 If the length of a simple pendulum is doubled what will be its new time period?
Mark (1)
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Q 2 A pendulum clock is observed to give correct time at the equator. What will happen
if the same pendulum clock is taken to the pole of the earth?
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Q 3 In which condition the motion of a simple pendulum is simple harmonic?
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Q 4 What is oscillatory motion?
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Q 5 What is periodic motion?
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Q 6 Is the damping force constant on a system executing SHM ?
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Q 7 Two simple pendulums of equal length cross each other at mean position. What is
their phase difference?
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Q 8 A vertical U-tube of uniform cross section contains water upto a height of 0.5m. If
water on one side is depressed a little and then released it performs SHM up and down.
Calculate (a) time period and (b) angular frequency of the vibration.
Marks (2)
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Q 9 If the period of oscillation of mass m suspended from a spring is 2s, find the period
of mass 4m?
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Q 10 A mass m is vertically suspended from a spring of negligible mass. The system
oscillates with a frequency v. Find the frequency of the system if a mass 4m is suspended
from the same spring?
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Q 11 A body of mass m is suspended by a spring of spring constant k. When the body is
depressed a little and released, find its frequency of oscillation?
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Q 12 Is rotation of earth about its axis is an example of SHM?
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Q 13 When displacement is one-fourth of the amplitude, find the fraction of the total
energy which is kinetic?
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Q 14 The piston in the cylinder head of a locomotive has a stroke (twice the amplitude)
of 1.0 m. If the piston moves with simple harmonic motion with an angular frequency of
300 rev/min, what is its maximum speed?
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Q 15 When the displacement is one half of the amplitude, find the fraction of total energy
which is potential?
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Q 16 The length of a simple pendulum executing SHM is increased by 21%. Find the
percentage increase in the time period of the pendulum of increased length?
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Q 17 At what distance from the mean position is the kinetic energy in simple harmonic
oscillaton equal to P.E ?
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Q 18 A simple pendulum of length l and having a bob of mass m is suspended in a car.
The car is moving on a circular track of radius r with a uniform speed v. If the pendulum
makes small oscillations in a radial direction about its equilibrium position what will be
its time period?
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Q 19 The total energy of a particle, executing SHM is independent of displacement.
Explain.
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Q 20 A block of mass 5 kg executes simple harmonic motion under the restoring force of
a spring. The amplitude and the time period of the motion are 0.1m and 3.14s
respectively. Find the maximum force exerted by the spring on the block.
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Q 21 A block is resting on a piston which is moving vertically with simple harmonic
motion of period 1.0s. At what amplitude of motion will the block and piston separate?
What is the maximum velocity of the piston at this amplitude?
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Q 22 A simple harmonic motion is represented by y = 10Sin(20t+0.5). Write down its
amplitude, angular frequency, frequency, time period and initial phase, if displacement is
in metres and time in seconds?
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Q 23 The potential energy of a particle oscillating on x-axis is given by U=20+(x-2)2
where U is in joules and x is in metres. Total mechanical energy of the particle is 36
joules.
(a) State whether the motion of the particle is simple harmonic or not?
(b) Find the mean position.
(c) Find the maximum kinetic energy of the particle.
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Q 24 A particle executes SHM with a time period of 2s and amplitude 5 cm. Find (a)
Displacement (b) Velocity (c) Acceleration after 1/3 seconds.
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Q 25 Between the plates of the capacitor with potential difference V across its plates such
that upper plate is negative. A ball with positive charge q and mass m is suspended by a
thread of length l. If the electrostatic force acting on the ball is less than the gravitational
force, what should be the period of the ball?
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Q 26 A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20
cm. A body suspended from this spring, when displaced and released, oscillates with
period of 0.60 seconds. What is the weight of the body?
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Q 27 A mass attached to a spring is free to oscillate, with angular frequency w, in a
horizontal plane without friction or damping. It is pulled to a distance x0 and pushed
towards the centre with a velocity v0 at a time t=0. Determine the amplitude of the
resulting oscillations in terms of the parameters w, x0 and v0.
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Q 28 A uniform cylinder of mass m and radius r is attached to one end of the spring as
shown in the fig on rough horizontal surface. If the cylinder is slightly displaced, then
find the time period of the oscillation given that there is no slipping on the surface.
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Q 29 A particle is performing simple harmonic motion along x-axis with amplitude 4.0
cm and time period 1.2s. What is the minimum time taken by the particle to move from x
=+2 cm to x =+4 cm and back again?
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