Engineering Physics Multiple Choice Questions on “Simple Harmonic Oscillation”.
1. The bob of the pendulum moves faster at the lowest position for a larger amplitude.
a) True
b) False
Answer: a
Clarification: We know that the velocity of a simple pendulum is maximum at the lowest position and is given by
vmax=ωA
That is for larges amplitude, the bob of the pendulum would move faster.
2. The total energy of a particle executing simple harmonic motion is ___________
a) ∝x
b) ∝x2
c) Independent of x
d) ∝√x
Answer: c
Clarification: E=2π2mv2A2
Clearly, the total energy is independent of displacement x.
3. A body executes simple harmonic motion. The potential energy, the kinetic energy and total energy are measured as a function of displacement x. Which of the following statements is true?
a) Kinetic energy is maximum when x = 0
b) Total energy is zero, when x = 0
c) Kinetic energy is maximum when x is maximum
d) Potential energy is maximum when x = 0
Answer: a
Clarification: The kinetic energy of a simple harmonic oscillator is maximum when x = 0.
4. Two simple motions are represented by
y1=5(sin2πt+√3 cos2πt)
y2=5sin(2πt+π/4)
The ratio of the amplitude of two simple harmonic motions is?
a) 1:1
b) 1:2
c) 2:1
d) 1:√3
Answer: c
Clarification: y1=5×2(sin2πtcos(π/3)+sin(π/3)cos2πt)
y1=10sin(2πt+(π/3))
y2=5sin(2πt+(π/4))
A1/A2 = 10/5=2:1.
5. The ratio of frequencies of two pendulums is 2:3 then their lengths are in ratio ___________
a) √(2/3)
b) √(3/2)
c) 4/9
d) 9/4
Answer: d
Clarification: v1/v2 = √(l2/l1)
l1/l2 = ((v2)2)/((v1)2)=9/4.
6. For a particle executing simple harmonic motion, which of the following statements is not correct?
a) Total energy is always directed toward a fixed point
b) Restoring force is always directed towards a fixed point
c) Restoring force is maximum at the extreme positions
d) Acceleration of the particle is maximum at the equilibrium position
Answer: d
Clarification: At the equilibrium position, the velocity of a particle in simple harmonic motion is maximum and consequently its acceleration is minimum.
7. If a spring of mass 30kg has a spring constant of 15N/m, then its time period is ___________
a) 2πs
b) 2√2 πs
c) 2√2π s
d) 2√2 s
Answer: b
Clarification: T=2π√(m/k)
T=2π√(30/15)=2π√2 s.
8. Statement: Water in a U-tube executes simple harmonic motion. The time period for mercury filled up to the same height in the U-tube be greater than that in case of water.
Reason: The amplitude of an oscillating pendulum goes on increasing.
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
Answer: d
Clarification: Both the statement and reason are false. Period of oscillation of a liquid in a U-tube is independent of the density of the liquid. The amplitude is the oscillating pendulum decreases due to air friction.
9. A spring (spring constant = k) is cut into 4 equal parts and two parts are connected in parallel. What is the effective spring constant?
a) 4k
b) 16k
c) 8k
d) 6k
Answer: c
Clarification: Spring constant of each one-fourth part = 4k
When two parts are connected in parallel,
kp=4k+4k=8k.
10. The periodic time of a body executing simple harmonic motion is 4s. After how many intervals from time t=0, its displacement will be half of its amplitude?
a) 1⁄2 s
b) 1/3 s
c) 1⁄4 s
d) 1/6 s
Answer: b
Clarification: t=1t/12=4/12=1/3 s.