Engineering Questions with Answers - Multiple Choice Questions

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# Oscillations – 1

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

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Answer: a

Explanation: Uniform circular motion is a periodic motion but not simple harmonic.

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

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Answer: b

Explanation: Wave moving through a string fixed at both ends has simple harmonic nature.

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

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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.

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)

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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.

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

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Answer: d

Explanation: vmax=2πvA

31.4=2×3.14v×5

v=1Hz.

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

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Answer: b

Explanation: y=asinωt

a/2=asin(2πt/T)

sin(2πt/T)=sin(π/6)

2πt/T=π/6

T=T/12.

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

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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.

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

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Answer: a

Explanation: a=-ω2 y

ω2=a/y=2/0.02=100

ω=10rad/s.

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

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Answer: c

Explanation: The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is π/2.

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

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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.