1. Which one of the following is a simple harmonic
motion
a) Wave moving through a string fixed at both ends
b) Earth spinning about its own axis
c) Ball bouncing between two rigid vertical walls
d) Particle moving in a circle with uniform speed
Explanation: Simple harmonic waves are set up in a string fixed at the, two ends.
2. A particle is moving in a circle with uniform
speed. Its motion is
a) Periodic and simple harmonic
b) Periodic but not simple harmonic
c) A periodic
d) None of the above
Explanation: Periodic but not simple harmonic
3.Two simple harmonic motions are represented by
the equations \[y_{1}=0.1\sin\left[100\pi t+\frac{\pi}{3}\right]\]
and
\[y_{2}=0.1\cos \pi t\] . The phase difference of the velocity
of particle 1 with respect to the velocity of
particle 2 is
a) \[\frac{-\pi}{3}\]
b) \[\frac{\pi}{6}\]
c) \[\frac{-\pi}{6}\]
d) \[\frac{\pi}{3}\]
Explanation:
4. Two particles are executing S.H.M. The equation
of their motion are \[y_{1}=10 \sin\left(\omega t+\frac{\pi T}{4}\right),y_{2}=25\sin \left(\omega t+\frac{\sqrt{3}\pi T}{4}\right)\]
What is
the ratio of their amplitude
a) 1 : 1
b) 2 : 5
c) 1 : 2
d) None of these
Explanation:
5. The periodic time of a body executing simple
harmonic motion is 3 sec. After how much interval
from time t = 0, its displacement will be half of
its amplitude
a) \[\frac{1}{8}sec\]
b) \[\frac{1}{6}sec\]
c) \[\frac{1}{4}sec\]
d) \[\frac{1}{3}sec\]
Explanation:
6. A system exhibiting S.H.M. must possess
a) Inertia only
b) Elasticity as well as inertia
c) Elasticity, inertia and an external force
d) Elasticity only
Explanation: Elasticity as well as inertia
7. If \[x=a \sin \left(\omega t+\frac{\pi}{6}\right)\] and \[x'=a \cos \omega t\] , then what is
the phase difference between the two waves
a) \[\pi/3\]
b) \[\pi/6\]
c) \[\pi/2\]
d) \[\pi\]
Explanation:
8. 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
a) \[\frac{\pi A\sqrt{3}}{T}\]
b) \[\frac{\pi A}{T}\]
c) \[\frac{\pi A\sqrt{3}}{2T}\]
d) \[\frac{3\pi^{2} A}{T}\]
Explanation: Velocity of a particle executing S.H.M. is given by
9.A body is executing simple harmonic motion with
an angular frequency 2 rad/ s . The velocity of the
body at 20 mm displacement, when the amplitude
of motion is 60 mm, is
a) 40 mm /s
b) 60 mm /s
c) 113 mm /s
d) 120 mm /s
Explanation:
10.A body of mass 5 gm is executing S.H.M. about a
point with amplitude 10 cm. Its maximum velocity
is 100 cm/sec. Its velocity will be 50 cm/sec at a
distance
a) 5
b) \[5\sqrt{2}\]
c) \[5\sqrt{3}\]
d) \[10\sqrt{3}\]
Explanation:
