## 1. Which of the following quantities remains constant during simple harmonic motion (SHM)?

### Answer:

### Explanation:

In SHM, although kinetic and potential energies change, their sum, which is the total mechanical energy, remains constant.

## 2. In a simple pendulum, at what position is the potential energy maximum?

### Answer:

### Explanation:

At the extreme position, the pendulum has reached its maximum displacement, and thus, its potential energy is at a maximum.

## 3. If the amplitude of a simple harmonic oscillator is doubled, its period will:

### Answer:

### Explanation:

The period of SHM does not depend on amplitude.

## 4. What kind of force acts on a body performing SHM?

### Answer:

### Explanation:

A restoring force proportional to its displacement and acting in the opposite direction is always acting on a body in SHM.

## 5. The time period of a simple pendulum of length L on the surface of Earth is T. What will be its time period on a planet where acceleration due to gravity is half of that on Earth?

### Answer:

### Explanation:

Time period T is directly proportional to 1/√g. If g is halved, T will become √2 times.

## 6. For a spring-block oscillator, the time period T is given by:

### Answer:

### Explanation:

The time period for a spring-block system is given by T = 2π√(m/k), where m is the mass and k is the spring constant.

## 7. Which of the following is a necessary condition for SHM?

### Answer:

### Explanation:

For SHM, the restoring force is zero at the mean position.

## 8. The displacement of a body performing SHM is given by x = A sin(ωt + φ). Here, φ represents:

### Answer:

### Explanation:

In the equation, φ represents the initial phase or phase constant.

## 9. The maximum velocity of a body in SHM is given by:

### Answer:

### Explanation:

The maximum velocity Vmax = ωA, where ω is the angular frequency and A is the amplitude.

## 10. In SHM, acceleration is directly proportional to:

### Answer:

### Explanation:

Acceleration in SHM is directly proportional to the displacement and is directed towards the mean position.

## 11. The potential energy of a harmonic oscillator is zero at:

### Answer:

### Explanation:

At the mean position, the displacement is zero; hence, potential energy is zero.

## 12. If the frequency of a harmonic oscillator is 10 Hz, its time period will be:

### Answer:

### Explanation:

Time period T = 1/frequency. Therefore, T = 1/10 = 0.1 s.

## 13. A body is in SHM. When its displacement is half of the amplitude, what fraction of its total energy is kinetic?

### Answer:

### Explanation:

When displacement is half of the amplitude, the kinetic energy is 3/4th of the total energy.

## 14. The angular frequency (ω) of a body in SHM is related to the time period (T) as:

### Answer:

### Explanation:

Angular frequency ω = 2π times the frequency, and frequency = 1/T. Thus, ω = 2π/T.

## 15. A body is oscillating with a time period of 2 seconds. Its frequency is:

### Answer:

### Explanation:

Frequency = 1/Time period. Therefore, frequency = 1/2 = 0.5 Hz.