Which of the following quantity does not change due to damping of oscillations?

Options

A. Angular frequency
B. Time period
C. Initial phase
D. Amplitude

Answer

To solve the question of which quantity does not change due to damping of oscillations, we can analyze the effects of damping on various parameters of oscillatory motion.

### Step-by-Step Solution:

1. **Understanding Damped Oscillation**:
- Damped oscillation refers to the oscillatory motion where the amplitude decreases over time due to the presence of a damping force (like friction or air resistance). This means that the system loses energy, leading to a gradual reduction in the amplitude of oscillations.

2. **Identifying Key Quantities**:
- The key quantities associated with oscillations include:
- Amplitude (A)
- Angular frequency (ω)
- Time period (T)
- Initial phase (φ)

3. **Effect of Damping on Amplitude**:
- The amplitude of the oscillation decreases over time due to damping. Therefore, the amplitude is not constant and changes as the system oscillates.

4. **Effect of Damping on Angular Frequency**:
- The angular frequency (ω) is related to the amplitude and the damping factor. As the amplitude decreases, the angular frequency also changes. Thus, angular frequency is not constant.

5. **Effect of Damping on Time Period**:
- The time period (T) of the oscillation is inversely related to the angular frequency (T = 2π/ω). Since the angular frequency changes with damping, the time period also changes.

6. **Effect of Damping on Initial Phase**:
- The initial phase (φ) of the oscillation is a fixed quantity that describes the starting position of the oscillating system at time t=0. It does not change due to damping, as it is determined by the initial conditions of the system.

7. **Conclusion**:
- Among the quantities discussed, the initial phase (φ) is the only one that remains unchanged due to damping. Therefore, the answer to the question is that the initial phase does not change due to damping of oscillations.

### Final Answer:
The quantity that does not change due to damping of oscillations is **initial phase (φ)**.