A particle executes simple harmonic motion with a frequency \(\nu.\) The frequency with which the kinetic energy oscillates is:
1. \(\nu/2\)
2. \(\nu\)
3. \(2\nu\)
4. zero

A particle executes simple harmonic motion under the restoring force provided by a spring. The time period is T. If the spring is divided in two equal parts and one part is used to continue the simple harmonic motion, the time period will

1. remain T

2. become 2T

3. become T/2

4. become T/\(\sqrt2\)

Two bodies \(A\) and \(B\) of equal mass are suspended from two separate massless springs of spring constant \(k_1\) and \(k_2\) respectively. If the bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of \(A\) to that of \(B\) is:

1. \(k_{1} / k_{2}\)

2. \(\sqrt{k_{1} / k_{2}}\)

3. \(k_{2} / k_{1}\)

4. \(\sqrt{k_{2} / k_{1}}\)

A spring-mass system oscillates with a frequency \(\nu.\) If it is taken in an elevator slowly accelerating upward, the frequency will:
1. increase
2. decrease
3. remain same
4. become zero

A spring-mass system oscillates in a car. If the car accelerates on a horizontal road, the frequency of oscillation will:
1. increase
2. decrease
3. remain same
4. become zero

A pendulum clock that keeps the correct time on the earth is taken to the moon. It will run: (Take \(g_{\text{moon}}=\dfrac{g_\text{earth}}{6}\))

A wall clock uses a vertical spring-mass system to measure the time. Each time the mass reaches an extreme position, the clock advances by a second. The clock gives the correct time at the equator. If the clock is taken to the poles it will:

A pendulum clock keeping correct time is taken to high altitudes:

The free end of a simple pendulum is attached to the ceiling of a box. The box is taken to a height and the pendulum is oscillated. When the bob is at its lowest point, the box is released to fall freely. As seen from the box during this period, the bob will

1. continue its oscillation as before

2. stop

3. will go in a circular path

4. move on a straight line

Select the correct statements.

(a) A simple harmonic motion is necessarily periodic.

(b) A simple harmonic motion is necessarily oscillatory.

(c) An oscillatory motion is necessarily periodic.

(d) A periodic motion is necessarily oscillatory.

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (c) and (d)

4. None of these