F-125, SECTOR-10, DLF, FARIDABAD
TC SHARMA
TEST - 1: Oscillations, Waves
Time: 1:30 Hours
MM: 30+20
1. Can a motion be oscillatory but not simple harmonic? If you answer is yes, give an
example and if not, explain why.
[1]
2. When are the displacement and velocity in the same direction in S.H.M.?
[1]
3. The maximum acceleration of a simple harmonic oscillator is a0 and the maximum velocity
is v0. What is the displacement amplitude?
[1]
4. A girl is swinging in the sitting position. How will the period of the swing change if she
stands up?
[1]
5. Why are army troops not allowed to march in steps while crossing a bridge?
[1]
6. Justify the following statements:
[2]
(a) The motion of an artificial satellite around the earth cannot be taken as S.H.M.
(b) The time period of a simple pendulum will get doubled if its length is increased four
times.
7. The frequency of oscillations of a mass m suspended by a spring is v1. If length of the
spring is cut to one-half, same mass oscillates with frequency v2. Determine value of
v2/v1.
[2]
8. The amplitude of a simple harmonic oscillator is doubled. How does this affect (i) periodic
time, (ii) maximum velocity, (iii) maximum acceleration and (iv) maximum energy?
[2]
9. Two simple harmonic motions are represented by the equations:
[2]
x1  5sin (2t   / 4), x2  5 2 (sin 2t  cos 2t )
What is the ratio of their amplitudes?
10. The bob of a simple pendulum is a hollow sphere filled with water. How will the period of
oscillation change if the water begins to drain out of the hollow sphere from a fine hole at
its bottom?
11. A simple pendulum is hung in a stationary lift and its periodic time is T. What will be the
effect on its periodic time T if (i) the lift goes up with uniform velocity v (ii) the lift goes up
with uniform acceleration a (iii) the lift comes down with uniform acceleration a?
12. Springs of spring constants k, 2k, 4k, 8k, ... are connected in series. A mass m kg is attached
to the lower end of the last spring and the system is allowed to vibrate. What is the time
period of oscillations? Given m = 40 g and k = 2.0 N cm–1.
[3]
13. A particle executes simple harmonic motion between x = – A and x = + A. The time taken
for it to go from 0 to A/2 is T1 and to go from A / 2 to A is T2. How are T1 and T2 related?
14. Plot the corresponding reference circle for each of the following simple harmonic motions.
Indicate the initial (t = 0) position of the particle, the radius of the circle, and the angular
speed of the rotating particle. For simplicity, the sense of rotation may be fixed to be
anticlockwise in every case (x is in cm and t is in s).
(i) x  2sin(3t   / 3) (ii) x  cos( / 6  t ) (iii) x  3sin(2t   / 4)
TC SHARMA 9910747370
(iv) x  2cos t.
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[3]
F-125, SECTOR-10, DLF, FARIDABAD
TC SHARMA
15. A cylindrical piece of cork of base area A and height h floats in a liquid of density
1. The
cork is depressed slightly and then released. Show that the cork oscillates up and down
simple harmonically with a period T  2 h , where  is the density of cork. (Ignore
1 g
damping due to viscosity of the liquid).
[3]
16. Multiple Choice Questions:
[10×2 = 20]
(i) A particle executing simple harmonic motion along y-axis has its motion described by
the equation y  A sin(t )  B. The amplitude of the simple harmonic motion is
(a) A
(b) B
(c) A + B
(d)
A B
(ii) Two pendulums have time periods T and 5T/4. They start SHM at the same time
from the mean position. What will be the phase difference between them after the
bigger pendulum completed one oscillation?
(a) 45°
(b) 90°
(c) 60°
(d) 30°
(iii) The amplitude of a particle executing simple harmonic motion with a frequency of 60
Hz is 0.01 m. The maximum value of acceleration of the particle is
(a) 144 2 m/s 2
(b) 12 m/s2
(c) 11 m/s2
(d) 169 m/s2
(iv) The displacement of an SHM doing oscillation when K.E. = P.E. (amplitude = 4 cm) is
(a) 2 2 cm
(b) 2 cm
(c) 1 cm
(d) 2 cm
2
(v) Natural length of spring is 60 cm and its spring constant is 4000 N/m. A mass of 20
kg is hung from it. The extension produced in the spring (Take g = 9.8 m/s2) is
(a) 4.9 cm
(b) 0.49 cm
(c) 9.4 cm
(d) 0.94 cm
(vi) If a particle is oscillating on the same horizontal plane on the ground,
(a) it has only kinetic energy but not potential energy (b) it has only potential energy but
no kinetic energy (c) it has both kinetic energy and potential energy (d) none of these
(vii) Frequency of oscillation is proportional to
3k
m
(a)
(b)
k
m
(c)
2k
m
(d)
m
3k
(viii) The graph of time period (T) of a simple pendulum versus its length (l) is
T
T
T
l
l
l
l
(a)
(b)
(c) T
(d)
(ix) The ratio of frequencies of two pendulums are 2 : 3, then their lengths are in ratio
(a)
2/3
(b)
3/ 2
(c) 4/9
(d) 9/4
(x) What is time period of a pendulum hanged in a satellite? (T is time period on earth)
(a) zero
TC SHARMA 9910747370
(b) T
(c) infinite
(d) T / 6
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F-125, SECTOR-10, DLF, FARIDABAD
TC SHARMA
ANSWERS
(i) (a)
(ii) (b)
(iii) (a)
(iv) (a)
(v) (a)
(vi) (c)
(vii) (a)
(viii) (a)
(ix) (d)
(x) (c)
TC SHARMA 9910747370
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