Two simple pendulums of lengths 5 m and 20 m respectively are given small linear displacement in one direction at the same time. They will again be in the phase when the pendulum of shorter length has completed .... oscillations.

There are _______ complete oscillations are shown in the graph below.

1. 3
2. 2.5
3. 3.5
4. 4

Select the correct statement(s) from the following:
I. Motion of a satellite and a planet is periodic as well as SHM.
II. Mass suspended by a spring executes SHM.
III. Motion of a simple pendulum is always SHM.

1. I, II, and III
2. I only
3. II only
4. I and II

The periodic time of a body executing simple harmonic motion is 3 sec. After how many intervals from time t = 0, its displacement will be half of its amplitude:

1.  sec
2.  sec
3. sec
4. sec

Force acting in simple harmonic motion is always:

1. Directly proportional to the square of the displacement
2. Inversely proportional to the displacement
3. Inversely proportional to the square of the displacement
4. Directly proportional to the displacement

Choose the correct statement from the following:
Assertion: In oscillatory motion, displacement of a body from equilibrium can be represented by sine or cosine function.
Reason: The body oscillates to and from about its mean position.

1. Assertion is correct, the reason is correct; the reason is not a correct explanation for assertion
2. Assertion is incorrect, the reason is correct
3. Assertion is correct, the reason is correct; the reason is a correct explanation for assertion
4. Assertion is correct, reason is incorrect

The displacement time graph of a particle executing S.H.M. is as shown in the figure:

The corresponding force-time graph will be:

Assertion: All small oscillations are simple harmonic.
Reason: Oscillations of a simple pendulum system are always simple harmonic whether the amplitude is small or large.

1. If both the assertion and reason are true but the reason is not the correct explanation of assertion.
2. If the assertion is false but the reason is true.
3. If both the assertion and the reason are true and the reason is the correct explanation of the assertion.
4. If the assertion is true, but the reason is false.

Two simple pendulums of length 1 m and 16 m respectively are given small displacements at the same time in the same direction. The number of oscillations ‘N’ of the smaller pendulum for them to be in phase again is:

1. 4 / 3
2. 3 / 4
3. 4
4. 1 / 16

Select the true statement(s) about SHM.
I. Acceleration display style alpha displacement is a sufficient condition for SHM.
II. Restoring force display style alpha displacement is a sufficient condition for SHM.

1. Both I and II are wrong
2. II only
3. I only
4. I and II

What is constant in S.H.M.?

1. Restoring force
2. Potential energy
3. Kinetic energy
4. Periodic time

In a simple pendulum, the period of oscillation T is related to the length of the pendulum l as:

Assertion: The amplitude of an oscillating pendulum decreases gradually with time
Reason: The frequency of the pendulum decreases with time.

1. Assertion is correct, the reason is incorrect
2. Assertion is incorrect, the reason is correct
3. Assertion is correct, the reason is correct; the reason is not a correct explanation for assertion
4. Assertion is correct, the reason is correct; the reason is a correct explanation for assertion

Vibrations, whose amplitudes of oscillations decrease with time are called:

1. Damped vibrations
2. Free vibrations
3. None of these
4. Forced vibrations
    

If the metal bob of a simple pendulum is replaced by a wooden bob, then its time period will:

1. Decrease
2. Increase
3. Remains the same
4. First increase, then decrease