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AL-MC-SHM / p.1
1.
(88-I-4)
A force F is applied to an initially stationary
A.
2
m
4k.
B.
2
m
.
2k
C.
2
m
.
k
D.
2
2m
.
k
E.
2
4m
.
k
particle from time t = 0. F varies sinusoidally with
time t as shown in the following graph :
Which of the following graphs best represents the
variation of the subsequent velocity v of the
particle with t?
3.
(88-I-9)
A body is suspended by a string and allowed to
swing as a simple pendulum. When it is move from
the north pole to the equator, its period will
2.
(88-I-7)
4.
A.
remain constant.
B.
decrease.
C.
increase.
D.
decrease and then increase.
E.
increase and then decrease.
(89-I-9)
Diagram NOT to scale
A block of mass m is attached to two identical
springs
S1 and S 2 as shown. The force
An object performs simple harmonic motion. A
ticker-tape stuck to it records its positions at
constant of the springs is k. If the block is made to
0.020 s intervals for the first half cycle. The
execute simple harmonic motion, the period will be
maximum speed of the object is
A.
0.71 m s-1
B.
2.36 m s-1
C.
0.83 m s-1
D.
4.71 m s-1
E.
9.42 m s-1
AL-MC-SHM / p.2
5.
(89-I-10)
8.
(91-I-7)
A particle of mass 0.2 kg moves with S.H.M. of
A piece of iron is suspended from a vertical spring.
amplitude 0.05 m. If the total energy of the particle
The iron (but not the spring) is immersed in a jar of
is 0.004 J, then its period of motion is
A.
B.
C.
D.
E.
 /4 s.
 /2 s.
3  /4 s.
 s.
2  s.
water, and oscillates with period
To . A vertical
sinusoidal force of variable period T is now
applied to the iron, using an electromagnet. Which
one of the following statements is NOT correct?
A.
When the electromagnet is switched
off, the period of the oscillations
6.
(90-I-7)
changes from T to
An object moves vertically with simple
harmonic motion just behind a wall. From the
B.
other side of the wall the object is visible in
The amplitude of the oscillations
increases greatly when T is brought
each cycle for 2.0 s and hidden behind the
close to
wall for 6.0 s. The maximum height reached
by the object relative to the top of the wall is
To .
C.
0.30 m. The amplitude of the motion is
To .
For any value of T, the water
temperature rises, due to energy
transferred from the electromagnet.
A.
0.18 m
B.
0.51 m
the water gains energy as the amplitude
C.
0.60 m
of the oscillations decreases.
D.
1.02 m
E.
1.20 m
D.
E.
If the electromagnet is switched off,
For T not close to
To , the forced
oscillations decrease slowly in
7.
(91-I-5)
amplitude due to damping.
A point mass is attached to the lower end of a light
spring fixed at the upper end. The mass is made to
oscillate vertically. If the potential energy of the
system is taken to be zero when the mass is at its
equilibrium position, the speed of the mass at the
equilibrium position is directly proportional to the
square root of
(1)
the amplitude of oscillation.
(2)
the total energy of the system.
(3)
the maximum potential energy of the system.
A.
(1), (2) and (3)
B.
(1) and (2) only
C.
(2) and (3) only
D.
(1) only
E.
(3) only
AL-MC-SHM / p.3
9.
(91-I-8)
11.
(93-I-6)
The period of a simple pendulum undergoing
simple harmonic motion may be increased by
A trolley attached to two fixed supports
S1 and
A.
using a heavier pendulum bob.
B.
increasing the amplitude of oscillation.
C.
placing the pendulum at the top of a
mountain.
S 2 by identical springs is displaced from the
D.
equilibrium position along the direction X and set
placing the pendulum at the North
pole.
into oscillation. A load is dropped onto and is
E.
retained by the trolley when it passes through its
shortening the string attached to the
bob.
equilibrium position P.Which of the following
statements is/are correct?
12.
(93-I-7)
A particle oscillates with simple harmonic motion
(1)
(2)
Linear momentum in the horizontal direction
along a straight line with amplitude A. When the
is conserved just before and after the load
displacement of the particle from its equilibrium
lands on the trolley.
position is 1/2 A, its speed is u. The speed of the
The amplitude of oscillation decreases after
particle when passing the equilibrium position is
the landing of the load.
(3)
The period increases after the landing of the
A.
2u / 3
B.
2u
C.
3u
load.
A.
(1), (2) and (3)
B.
(1) and (2) only
C.
(2) and (3) only
D.
D.
(1) only
E.
E.
(3) only
2u
4u
13. (94-IIA-8)
10.
(92-I-4)
A small mass is hung vertically from a light spring
An object is placed on a horizontal platform
fixed at its upper end. When the mass is pulled
vibrating vertically in S.H.M. with a period of
down 1 cm from its equilibrium position and
0.2 s. The maximum amplitude of oscillation
released from rest, it takes 0.3 s to rise back to its
which will allow the object to remain in contact
equilibrium position. If the mass is pulled down 2
with the platform throughout the motion is
cm from its equilibrium position and released from
rest, how long does it take for the mass to rise 1 cm?
(Assume that the spring obeys Hooke’s law.)
A.
1 cm
B.
5 cm
C.
10 cm
A.
0.30 s
D.
100 cm
B.
0.25 s
E.
indeterminate
C.
0.20 s
D.
0.15 s
E.
0.10 s
AL-MC-SHM / p.4
14. (94-IIA-9)
16.
(96-IIA-5)
Which of the following physical quantities will
decrease with time in damped harmonic motion?
15.
(1)
Period
(2)
Amplitude
(3)
Mechanical energy
A.
(1) only
The figure shows two blocks A and B, each of
B.
(3) only
mass m, connected by two light springs to a fixed
C.
(1) and (2) only
support. Each spring has a force constant k. What
D.
(2) and (3) only
is the total extension of the system when it is at
E.
(1), (2) and (3)
static equilibrium?
(95-IIA-7)
17.
A simple pendulum is displaced an angle

and
is released from rest. If T is the tension in the
string and m is the mass of the bob, which of the
following statements is/are correct?
A.
mg /(2 k)
B.
mg /k
C.
3 mg /(2k)
D.
2 mg /k
E.
3 mg /k
(96-IIA-9)
A system A oscillating at its natural frequency
fA
is coupled to a system B of natural frequency
fB ,
and causes system B to oscillate. When the steady
(1)
(2)
At the moment when the bob is released,
state is reached, which of the following statements
T cos   mg
is/are correct?
The restoring force of the harmonic motion
is
(3)
T sin  .
The period of oscillation is independent of

when

is small.
A.
(1) only
B.
(3) only
C.
(1) and (2) only
D.
(2) and (3) only
E.
(1), (2) and (3)
fA.
(1)
System B oscillates at frequency
(2)
The amplitude of system B depends on the
difference of
(3)
f A and f B .
The rate of transfer of energy from system A
to B is high when
f A is close to f B .
A.
(1) only
B.
(3) only
C.
(1) and (2) only
D.
(2) and (3) only
E.
(1), (2) and (3)
AL-MC-SHM / p.5
18. (96-IIA-10)
21.
(98-IIA-8)
A metre rule is clamped horizontally to the edge of a
A body hanging on a light spring oscillates
bench so that most of its length overhangs and it is
vertically between levels X and Z as shown below.
free to vibrate with vertical simple harmonic motion.
Its static equilibrium position is at level Y.
The tip of the rule vibrates with am amplitude of
1
3.5 cm and a maximum speed of 1.0ms . What is
the frequency of vibration of the rule?
A.
3.0 Hz
B.
3.5 Hz
C.
4.0 Hz
D.
4.5 Hz
E.
5.0 Hz
Which of the following statements is/are correct?
(1) The acceleration of the body is zero when it is
19. (97-IIA-8)
at level X.
A 50-g mass suspended from a light helical spring
oscillates with vertical simple harmonic motion of
amplitude 2.5 cm. If the maximum kinetic energy
of the mass is 3.0 x10
oscillation is
3
J , its frequency of
(2) The strain energy of the spring is zero when the
body is at level Y.
(3) The net downward force acting on the body is
at its maximum when it is at level Z.
A. (1) only
A.
0.4 Hz
B.
(3) only
B.
0.8 Hz
C.
(1) and (2) only
C.
1.1 Hz
D. (2) and (3) only
D.
1.9 Hz
E.
E.
2.2 Hz
20. (97-IIA-9)
When a body performs a simple harmonic motion,
which of the following is/are correct?
(1)
Displacement from the equilibrium position
is
(2)
 /2
out of phase with the velocity.
Acceleration is
 /2
out of phase with the
velocity.
(3)
Displacement from the equilibrium position
is in phase with the acceleration.
A.
(1) only
B.
(3) only
C.
(1) and (2) only
D.
(2) and (3) only
E.
(1), (2) and (3)
(1), (2) and (3)
AL-MC-SHM / p.6
22.
(98-IIA-9)
24.
(99-IIA-9)
A mass is suspended by a light spring fixed to the
ceiling. When the mass-spring system undergoes
vertical oscillation freely, its frequency is
f o . If
the system is removed from the ceiling and forced
to oscillate vertically by a periodic driving force of
The above graph shows the variation of the
variable frequencies, which of the following
acceleration a of a particle with its displacement x
graphs best represents the relationship between its
from a fixed point. Which of the following graphs
frequency of oscillation, f , and the applied
shows the variation of its potential energy U with
frequency,
x?
fa ?
25.
(00-IIA-10)
A small block of mass 0.1 kg is suspended from
the ceiling by a light spring of force constant
23.
(99-IIA-4)
12 Nm-1. If the block is projected vertically
.
The velocity of an object changes with time but the
downwards with a speed of 0.5 ms-1 from its
magnitude of its acceleration remains unchanged.
equilibrium position, what is the maximum
The motion of the object can be
acceleration of the block in its subsequent motion?
(1)
simple harmonic motion.
A.
5.0 ms-2
(2)
parabolic motion of a projectile.
B.
5.5 ms-2
(3)
uniform circular motion.
C.
6.0 ms-2
D.
6.5 ms-2
E.
7.0 ms-2
A.
(1) only
B.
(3) only
C.
(1) and (2) only
D.
(2) and (3) only
E.
(1), (2) and (3)
AL-MC-SHM / p.7
26.
(00-IIA-13)
28.
(01-IIA-7)
The maximum speed of a simple harmonic
oscillator is 1ms-1 and its amplitude is 0.5 m. What
is the speed of the oscillator when its displacement
from the equilibrium position is 0.3 m?
On a smooth horizontal surface, a block connected
A.
0.2 ms 1
to the wall with a light spring performs simple
B.
0.36 ms 1
harmonic motion of amplitude A as shown. If the
C.
0.4 ms 1
amplitude is reduced to A/2, which of the
D.
0.6 ms 1
following quantities would be halved?
E.
0.8ms 1
(1)
the maximum velocity of the block
(2)
the maximum elastic potential energy stored
An object undergoes a simple harmonic motion
in the spring
with an amplitude A, and its total energy is E.
the period of oscillation of the block
What is the displacement of the object from the
(3)
29.
(02-IIA-9)
equilibrium position when its kinetic energy is
A.
(1) only
B.
(3) only
C.
(1) and (2) only
D.
(2) and (3) only
E.
27.
(1), (2) and (3)
(01-IIA-6)
3E
4 ?
A.
A
2
B.
A
4
C.
3A
4
For an object oscillating with simple harmonic
motion, which of the following quantities will
reach the maximum value when the object is at its
maximum displacement?
(1) the restoring force acting on the object
(2) the total potential energy of the system
(3) the speed of the object
A. (1) only
B. (3) only
C. (1) and (2) only
D. (2) and (3) only
E. (1), (2) and (3)
3A
D.
2
AL-MC-SHM / p.8
30.
(02-IIA-10)
32.
(03-IIA-8)
An object vibrates with simple harmonic motion.
Which of the following will be doubled when the
amplitude is doubled?
The graph describes the motion of s simple
A.
the maximum potential energy
B.
the maximum momentum
C.
the period of oscillation
D.
the total mechanical energy
harmonic oscillator. Which pair of physical
quantities is most likely represented by variables y
33.
and x.
.
y
x
A.
Displacement
Acceleration
B.
Force
Displacement
C.
Kinetic Energy
Displacement
D.
Speed
Displacement
(03-IIA-9)
A light spring is mounted horizontally with one
end fixed to a wall and the other end attached to a
31.
(03-IIA-7)
block. The block is set to oscillate on a smooth
horizontal surface as shown. When the block is at
its greatest displacement from the wall, a lump of
plasticine is placed lightly on it so that they move
together in the subsequent motion. Which of the
following physical quantities of the system would
become smaller?
A simple pendulum is pulled horizontal and then
released from rest with the string taut. Which of
A.
the amplitude of oscillation
the following statements about the tension in the
B.
the period of oscillation
string is not correct when the pendulum reaches
C.
the maximum acceleration of the system
its vertical position?
D.
the total mechanical energy of the system
A.
The tension equals the weight of the
pendulum bob in magnitude.
B.
The tension attains its greatest value.
C.
The tension does not depend on the length of
the pendulum.
D.
The tension depends on the mass of the
pendulum bob.
AL-MC-SHM / p.9
34.
(03-IIA-10)
A certain periodic driving force is applied to a
system which has a natural frequency of oscillation.
This results in the oscillation of the system. What
would happen if the frequency of the periodic
driving force is not close to the natural frequency
of the system?
(1)
The system would eventually oscillate at the
frequency of the driving force if some
damping forces are present.
(2)
The amplitude of oscillation would become
infinite if there are no damping forces.
(3)
The displacement of the system from its
equilibrium position would always be in
phase with the driving force.
A.
(1) only
B.
(3) only
C.
(1) and (2) only
D.
(2) and (3) only