Simple Harmonic Motion Test

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Simple Harmonic Motion Test - 20

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Question 1
1 / -0

The shape of the graph plotted between the velocity and the position of a particle executing simple harmonic motion is:

A
A straight line

B
An ellipse

C
A parabola

D
A hyperbola

Solution

The shape of the graph plotted between the velocity and the position of a particle executing simple harmonic motion is an ellipse.
Question 2
1 / -0

Select the wrong statement about simple harmonic motion.

A
The body is uniformly accelerated.

B
The velocity of the body changes smoothly at all instants.

C
The amplitude of oscillation is symmetric about the equilibrium position.

D
The frequency of oscillation is independent of amplitude.

Solution

In a simple harmonic motion, the acceleration varies with displacement.
Question 3
1 / -0

A particle is executing SHM with time period T starting from the mean position. The time taken by it to complete 5/8 oscillations is:

A
T/12

B
T/6

C
5T/12

D
7T/12

Solution

Total distance covered by the particle in one oscillation = 4A

We divide the whole path into 8 intervals of A/2.

So,

Total time taken = time to complete previous one half (2A) + time to complete A/2 = T/2 + T/12 = 7T/12
Question 4
1 / -0

A particle is executing S.H.M. between x = ± A. The time taken to go from 0 to A/2 is T₁ and to go from A/2 to A is T_2, then:

A
T₁< T₂

B
T₁> T₂

C
T₁= T₂

D
T₁= 2T₂

Solution
Question 5
1 / -0

For a particle executing simple harmonic motion, the amplitude is A and the time period is T. The maximum speed will be:

A
4AT

B
2A/T

C

D
2πA/T

Solution
Question 6
1 / -0

A particle is executing S.H.M with an amplitude A and has maximum velocity v_0, its speed at displacament 3A/4 will be :

A

B

C
v₀

D

Solution

The equation of displacement from the mean position be x = Asinωt
Question 7
1 / -0

Two particles executing SHM of the same frequency meet at x = +a/2 while moving in opposite directions. The phase difference between the particles is:

A
π/6

B
π/3

C
5π/6

D
2π/3

Solution
Question 8
1 / -0

The displacements of two particles executing SHM on the same line are given as

The phase difference between them at t=1 sec is:

A
π

B
π/2

C
π/4

D
π/6

Solution

From these equations, it is clear that phase difference = π/6
Question 9
1 / -0

For a particle showing motion under the force F= -5 (x - 2)², the motion is:

A
Translatory

B
Oscillatory

C
SHM

D
All of these

Solution

Here given, F = −5 (x−2)²

Force is always negative, irrespective of the displacement. So the given motion is translatory.
Question 10
1 / -0

For a particle showing motion under the force F= -5(x - 2), the motion is:

A
Translatory

B
Oscillatory

C
SHM

D
Both (2) & (3)

Solution

Given. F = -5(x-2)

This represents the SHM with the mean position at x = 2. Since SHM is an oscillatory motion. The given equation represents oscillatory motion and SHM.