Define amplitude of `S.H.M.` ? Does Amplitude affect the time period ?

Answer

### Step-by-Step Solution:

1. **Definition of Amplitude**:
- Amplitude in Simple Harmonic Motion (S.H.M.) is defined as the maximum displacement of the oscillating object from its mean (equilibrium) position.
- It represents how far the object moves from the center point during its motion.

2. **Visual Representation**:
- Consider a graph where the horizontal line represents the mean position. The points where the object reaches its maximum displacement in either direction (positive and negative extremes) are the points of amplitude.
- The distance from the mean position to either of these extreme points is the amplitude.

3. **Mathematical Expression**:
- If we denote the amplitude as 'A', then:
- The maximum positive displacement = +A
- The maximum negative displacement = -A
- Thus, the amplitude is the absolute value of the maximum displacement from the mean position.

4. **Effect of Amplitude on Time Period**:
- The time period (T) of S.H.M. is given by the formula:
\[ T = \frac{2\pi}{\omega} \]
where \(\omega\) is the angular frequency.
- In this equation, amplitude does not appear. This indicates that the time period is independent of the amplitude.

5. **Conclusion**:
- Therefore, while amplitude is a crucial characteristic of S.H.M. indicating the extent of motion, it does not influence the time period of the oscillation.