# Engineering Physics Questions and Answers – Periodic Motion

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

1. A motion can be periodic and not oscillatory.
a) True
b) False

Explanation: A motion can be periodic and not oscillatory. For example, uniform circular motion is periodic but not oscillatory.

2. A simple pendulum of length l and with a bob whose mass is m is moving along a circular arc of angle θ in a vertical plane. A sphere of mass m is placed at the end of the circle. What momentum will be given to the sphere by the moving bob?
a) Infinity
b) Constant
c) Unity
d) Zero

Explanation: The momentum given to the sphere by the moving bob is zero because the velocity of the bob at the end of the arc will be zero.

3. When a 2 kg body is suspended by a spring, the spring is stretched. If the body is pulled down slightly and released, it oscillates up and down. What force is applied on the body by the spring when it passes through the mean position?
a) Force equal to the gravity
b) Force equal to the pull
c) Conservative force
d) Force equal to the weight of the body

Explanation: At the mean position, there is no acceleration in the body, hence the resultant force applied by the spring will be exactly equal to the weight of the body.

4. The displacement of an object attached to a spring and executing simple harmonic motion is given by x = 2×10-2 cosπt(in m). The time at which the maximum speed first occurs is?
a) 0.5s
b) 0.75s
c) 0.125s
d) 0.25s

Explanation: Displacement, x = 2×10-2 cosπt
Velocity, v = dx/dt=-2×10-2 πsinπt
Velocity becomes maximum when
Sinπt=1
πt=π/2
T=0.5s.

5. The maximum velocity of a particle, executing simple harmonic motion with amplitude 7mm, is 4.4m/s. The period of oscillation is?
a) 0.01s
b) 0.1s
c) 10s
d) 100s

Explanation: vmax=ωA=2π/T×A
T=2πA/vmax = (2×22×7×10-3)/(7×4.4)=.01s.
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6. If the frequency of oscillation of a particle doing simple harmonic motion is n, the frequency of kinetic energy is?
a) 2n
b) n
c) n/2
d) 2/n

Explanation: In one oscillation, the energy of the oscillation twice becomes kinetic and twice potential. Frequency of kinetic energy = 2n.

7. 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=9.8m/s2) is?
a) 4.9cm
b) 0.49cm
c) 9.4cm
d) 0.94cm

Explanation: In equilibrium, kx=mg
x=mg/k=(20×9.8)/9000=0.049m=4.9cm.

8. The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is ___________
a) 0.5π
b) π
c) 0.707 π
d) 0.61 π

Explanation: In a simple harmonic motion, instantaneous acceleration is ahead of instantaneous velocity in phase by π/2 rad.

9. A horizontal platform with an object placed on it is executing simple harmonic motion in the vertical direction. The amplitude of oscillation is 3.92×10-3 m. What must be the least period of these oscillations, so that the object is not detached from the platform?
a) 0.1256s
b) 0.1356s
c) 0.1456s
d) 0.1556s

Explanation: For an object to get detached from the platform,
amax ≤g or ω2 A≤g
(2π/T)2 A≤g
Tmin=2π√(A/g)=2π√((3.92×10-3)/9.8)
Tmin=2π×2×10-2=0.1256s.

10. Statement: The amplitude of an oscillating pendulum decreases gradually with time.
Reason: The frequency of the pendulum decreases with time.
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: The statement is true but the reason is false. Due to the friction of air, the amplitude gradually decreases with time.

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