Engineering Questions with Answers - Multiple Choice Questions
Oscillations – 1
1 - Question
The circular motion of a particle whose speed is constant is ________________
a) Periodic but not simple harmonic
b) Simple harmonic but not periodic
c) Periodic and simple harmonic
d) Neither periodic not simple harmonic
View Answer
Answer: a
Explanation: Uniform circular motion is a periodic motion but not simple harmonic.
2 - Question
Which of the following is a simple harmonic motion?
a) Particle moving in a circle with uniform speed
b) Wave moving through a string fixed at both ends
c) Earth spinning about its axis
d) Ball bouncing between two vertical walls
View Answer
Answer: b
Explanation: Wave moving through a string fixed at both ends has simple harmonic nature.
3 - Question
A particle executes simple harmonic motion along the x-axis. The force acting on it is given by?
a) Acos(kx)
b) Ae(-kx)
c) Akx
d) –Akx
View Answer
Answer: d
Explanation: F=-Akx implies that the force is proportional or displacement and acts in its opposite direction. So it represents simple harmonic motion.
4 - Question
Which one of the following represents simple harmonic motion?
a) Acceleration = kx
b) Acceleration = k0 x+k1 x2
c) Acceleration = -k(x+a)
d) Acceleration = k(x+a)
View Answer
Answer: c
Explanation: Acceleration = -kX, X = x+a
Thus the acceleration is proportional to displacement and acts in its opposite direction. Hence, acceleration = -k(x+a) represents simple harmonic motion.
5 - Question
A particle executing simple harmonic motion of amplitude 5cm has a maximum speed of 31.4 cm/s. The frequency of its oscillation is?
a) 4Hz
b) 3Hz
c) 2Hz
d) 1Hz
View Answer
Answer: d
Explanation: vmax=2πvA
31.4=2×3.14v×5
v=1Hz.
6 - Question
A particle executes simple harmonic oscillation. Its amplitude is a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is___________
a) T/8
b) T/12
c) T/2
d) T/4
View Answer
Answer: b
Explanation: y=asinωt
a/2=asin(2πt/T)
sin(2πt/T)=sin(π/6)
2πt/T=π/6
T=T/12.
7 - Question
A simple harmonic oscillator has an amplitude A and time period T. The time require by it to travel from x = A to x = A/2 is ___________
a) T/6
b) T/4
c) T/3
d) T/2
View Answer
Answer: a
Explanation: As the oscillator starts from x=A, we can take
x=acosωt
a/2=acos(2πt/T)
cos(2πt/T)=1/2=cos(π/6)
2πt/T=π/6
or t=T/6.
8 - Question
If a simple harmonic oscillator has got a displacement of 0.02m and acceleration equal to 2m/s2 at any time, the angular frequency of the oscillator is equal to ___________
a) 10 rad/s
b) 0.1 rad/s
c) 100 rad/s
d) 1 rad/s
View Answer
Answer: a
Explanation: a=-ω2 y
ω2=a/y=2/0.02=100
ω=10rad/s.
9 - Question
The phase difference between the acceleration of a particle executing simple harmonic motion and the instantaneous velocity is?
a) π
b) 0.707π
c) Zero
d) 0.5π
View Answer
Answer: c
Explanation: The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is π/2.
10 - Question
Which one of the following statements is true for the speed v and the acceleration of a particle executing simple harmonic motion?
a) When c is maximum, a is maximum
b) Value of a is zero, whatever may be the value of v
c) When v is zero, a is zero
d) When v is maximum, a is zero
View Answer
Answer: d
Explanation: In a simple harmonic motion, acceleration is ahead of velocity in phase by π/2 rad. So when velocity is maximum, acceleration is zero and vice versa.