# Engineering Physics Questions and Answers – Oscillatory Motion – 1

This set of Engineering Physics Multiple Choice Questions & Answers (MCQs) focuses on “Oscillatory Motion – 1”.

1. The motion of the earth about its axis is periodic and simple harmonic.
a) True
b) False

Explanation: The earth takes 24 hours to complete its rotation about its axis, but the concept of to and fro motion is absent, and hence the rotation of the earth is periodic and not simple harmonic.

2. An object of mass 0.2kg executes simple harmonic motion along the x-axis with a frequency of (25/π)Hz. At the position x = 0.04, the object has kinetic energy of 0.5J and potential energy 0.4J. The amplitude of oscillation is?
a) 6cm
b) 4cm
c) 8cm
d) 2cm

Explanation: Total energy,
E=2π2 mv2 A2
0.5+0.4=2π2×0.2×(25/π)2 A2
A2=0.9/(0.4×252)
A=3/(2×25)=3/50 m=6cm.

3. A spring of force constant 800N/m has an extension of 5cm. The work done in extending it from 5cm to 15cm is?
a) 8J
b) 16J
c) 24J
d) 32J

Explanation: At x1 = 5 cm,
U1=1/2×k(x1)2=1/2×800×0.052=1J
At x2=15cm,
U2=1/2×k(x2)2=1/2×800×0.152=9J
W=U2-U1=9-1=8J.

4. A simple pendulum is attached to the roof of a lift. If the time period of oscillation, when the lift is stationary is T, then the frequency of oscillation when the lift falls freely, will be ___________
a) Zero
b) T
c) 1/T
d) ∞

Explanation: In a freely falling lift,
g=0
v=1/2π×√(g/l)=1/2π×√(0/l)=0.

5. There is a simple pendulum hanging from the ceiling of a lift. When the lift is standstill, the time period of the pendulum is T. If the resultant acceleration becomes g/4, then the new time period of the pendulum is?
a) 0.8T
b) 0.25T
c) 2T
d) 4T

Explanation: T=2×√(l/g)
T=2π×√((l/g)/4)
T=2T.
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6. A lightly damped oscillator with a frequency v is set in motion by a harmonic driving force of frequency v’. When v’ is lesser than v, then the response of the oscillator is controlled by ___________
a) Spring constant
b) Inertia of the mass
c) Oscillator frequency
d) Damping coefficient

Explanation: Frequency of driving force is lesser than frequency v of a damped oscillator. The vibrations are nearly in phase with the driving force and response of the oscillator is controlled by spring constant.

7. Statement: In simple harmonic motion, the velocity is maximum, when the acceleration is minimum.
Reason: Displacement and velocity in simple harmonic motion is differ in phase by π/2.
a) Both statement and reason are true and the reason is the correct explanation of the statement
b) Both statement and reason are true but the reason is not the correct explanation of the statement
c) Statement is true, but the reason is false
d) Statement and reason are false

Explanation: Both statement and reason are true but the reason is not the correct explanation of the statement, In fact, the phase difference between velocity and acceleration is π/2.

8. What is the time period of a pendulum hanged in a satellite? (T is the time period on earth)
a) Zero
b) T
c) Infinite
d) T/√6

Explanation: In a satellite, g= 0
T=2π√(l/g)=2π√(l/0)=∞.

9. Which of the following functions represents a simple harmonic oscillation?
a) sinωt-cosωt
b) sinωt+sin2ωt
c) sinωt-sin2ωt
d) sin2 ωt

Explanation: y=sinωt-cosωt
dy/dt=ωcosωt+ωsinωt
(d2 y)/dt2 =-ω2 sinωt+ω2 cosωt
=-ω2 (sinωt-cosωt)
a=-ω2 y that is a∝y
This satisfies the condition of simple harmonic motion.

10. The displacement of a simple harmonic motion doing oscillation when kinetic energy = potential energy (amplitude = 4cm) is?
a) 2√2cm
b) 2cm
c) 1/√2 cm
d) √2 cm

Explanation: When kinetic energy = potential energy,
y=a/√2=4/√2=2√2 cm.

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