Simple Harmonic Motion Test

Result

Simple Harmonic Motion Test - 8

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

A cylindrical piston of mass M slides smoothly inside a long cylinder closed at one end, enclosing a certain mass of gas. The cylinder is kept with its axis horizontal. If the piston is disturbed from its equilibrium position, it oscillates simple harmonically. The period of oscillation will be

A

B

C

D

Solution

Let the piston be displaced through distance x towards left, then volume decreases, pressure increases. If ∆P is increase in pressure and ∆V is decrease in volume, then considering the process to take place gradually (i.e. isothermal)

This excess pressure is responsible for providing the restoring force (F) to the piston of mass M.
Question 2
1 / -0

The metallic bob of a simple pendulum has the relative density ρ. The time period of this pendulum is T. If the metallic bob is immersed in water, then the new time period is given by

A

B

C

D

Solution

When the bob is immersed in water ,

its effective weight =
Question 3
1 / -0

The velocity-time diagram of a harmonic oscillator is shown in the adjoining figure. The frequency of oscillation is

A
25 Hz

B
50 Hz

C
12.25 Hz

D
33.3 Hz

Solution
Question 4
1 / -0

A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is 20 m/s² at a distance of 5 m from the mean position. The time period of oscillation is:

A
2π s

B
π s

C
2 s

D
1 s

Solution

The acceleration is directly proportional to the displacement of the pendulum from the mean position.

Step 1: Find the angular velocity of the pendulum.

Step 2: Find the time period of the pendulum.
Question 5
1 / -0

A particle is executing a simple harmonic motion. Its maximum acceleration is α and maximum velocity is β. Then its time period of vibration will be:

A

B

C

D

Solution

The acceleration is maximum at the extreme position and the velocity at the mean position.

Step 1: Find the maximum acceleration.

For a particle executing SHM, we have maximum acceleration,
α = Aω² ... (i)

Step 2: Find the maximum velocity.

Maximum velocity, β = Aω …(ii)

Step 3: Find the time period of the particle.

Dividing Eq. (i) by Eq. (ii), we get:
Question 6
1 / -0

A particle is executing SHM along a straight line. Its velocities at distances x₁ and x₂ from the mean position are v₁ and v₂, respectively. Its time period is:

A

B

C

D

Solution

Hint: Use the relation between the velocity and the displacement.

Step 1: Find the velocity at x₁ and x_2.

Let A be the amplitude of oscillation then,

Step 2: Find the time period of the particle.
Subtracting Eq. (ii) from Eq. (i), we get:
Question 7
1 / -0

The oscillation of a body on a smooth horizontal surface is represented by the equation, X = A cos (ωt)

where X = displacement at time t
ω = frequency of oscillation
Which one of the following graphs shows correctly the variation 'a' with 't'?
Here a = acceleration at time t
T = time period

A

B

C

D

Solution

x = A cos(ωt)

Differentiating w.r.t t, we will get the velocity of the wave,
Question 8
1 / -0

Out of the following functions, which represent/s SHM?

A
Only (IV) does not represent SHM

B
(I) and (III)

C
(I) and (II)

D
Only (I)

Solution

Hint: For a simple harmonic motion, acceleration∝−y.

Step 1: Find the acceleration in each case.

Step 2: Identify the equations representing SHM.
Question 9
1 / -0

A simple pendulum performs simple harmonic motion about x = 0 with an amplitude a and time period T. The speed of the pendulum at x = a/2 will be:

A

B

C

D

Solution

Hint: The velocity of SHM depends on the displacement.

Step 1: Find the relation between the velocity and the displacement.
Question 10
1 / -0

Which one of the following equations of motion represents simple harmonic motion where k, k₀, k_1, and a are all positive?

A
Acceleration = -k₀x + k₁x²

B
Acceleration = -k(x + a)

C
Acceleration = k(x + a)

D
Acceleration = kx

Solution

Hint: The acceleration is proportional and opposite to the displacement.

Step 1: Find the equation of SHM.

General equation of SHM,