# Engineering Physics Questions and Answers – Harmonic Motion – 2

This set of Engineering Physics MCQs focuses on “Harmonic Motion – 2”.

1. Every simple harmonic motion is periodic motion, but every periodic motion need not be simple harmonic motion.
a) True
b) False

Explanation: Every simple harmonic motion is periodic motion, but every periodic motion need not be simple harmonic motion. For example, when the motion of the earth around the sun is a periodic motion, but not simple harmonic motion as the back and forth motion is not taking place.

2. A pendulum watch can be used in an artificial satellite.
a) True
b) False

Explanation: A pendulum watch cannot be used in an artificial satellite. In an artificial satellite, a body is in a state of weightlessness, that is g=0.
T=2π√(l/g)=∞
Inside the satellite, the pendulum does not oscillate. Hence a pendulum watch cannot be used in an artificial satellite.

3. A spring of force constant k is cut into two pieces, such that one piece is double the length of the other. Then the long piece will have a force constant of ___________
a) (2/3) k
b) (3/2) k
c) 3k
d) 6k

Explanation: Force constant, k = F/x
The length of the long piece is 2x/3
So, its force constant is
k=F/(2x/3)=3F/2x=3/2×k.

4. In a simple harmonic oscillator, at the mean position ___________
a) Kinetic energy in minimum, potential energy is maximum
b) Both kinetic and potential energies are maximum
c) Kinetic energy is maximum, potential energy is minimum
d) Both kinetic and potential energies are minimum

Explanation: At mean position, the kinetic energy is maximum and potential energy is minimum.

5. What is the maximum acceleration of the particle executing the simple harmonic motion, y = 2sin[(πt/2)+φ], where y is in cm?
a) π/2 cm/s2
b) π2/2 cm/s2
c) π/4 cm/s2
d) π2/4 cm/s2

Explanation:
y=2sin⁡[(πt/2)+] y=Asin(ωt+φ)
amax2 A=π2/2 cm/s2.
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6. When the maximum kinetic energy of a simple pendulum is K, then what its displacement (in terms of amplitude a) when its kinetic energy is K/2?
a) a/√2
b) a/2
c) a/√3
d) a/3

Explanation: Here Kmax=1/2×ka2=K
Let
1/2×ky2=K/2=1/2×1/2×ka2
y=a/√2.

7. The mass and the radius of a planet are twice that of earth. Then, period of oscillation of a second pendulum on that planet will be ___________
a) 1/√2s
b) 2√2s
c) 2s
d) 1/2s

Explanation: On earth,
g=GM/R2
On planet,
g=G2M/(4R)2 = g/2
T/T=√(g/g) = √((g/g)/2) = √2
T=√2×T=2√2 s.

8. In case of a forced vibration, the resonance wave becomes very sharp when the ___________
a) Applied periodic force is small
b) Quality factor is small
c) Damping force is small
d) Restoring force is small

Explanation: Lesser the damping force, more sharp is the resonance peak.

9. Statement: In simple harmonic motion, the motion is to and fro and periodic.
Reason: Velocity of the particle,
v=ω√(a2-x2)
Where x is displacement.
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 a correct explanation. Simple harmonic motion is a periodic motion in which acceleration is proportional to displacement from mean position and acceleration acts in the opposite direction of displacement.

10. If the metal bob of a simple pendulum is replaced by a wooden bob, then its time period will ___________
a) Increase
b) Decrease
c) Remains the same
d) First increases and then decreases

Explanation: Time period, T=2π√(l/g) is independent of the mass of the bob.

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