Can we use the equation `v = u +` at in SHM or not ?

Explanation

To determine whether we can use the equation \( v = u + at \) in Simple Harmonic Motion (SHM), we need to analyze the nature of acceleration in SHM.

### Step-by-Step Solution:

1. **Understanding the Equation**: The equation \( v = u + at \) is one of the equations of motion, where:
- \( v \) = final velocity
- \( u \) = initial velocity
- \( a \) = acceleration (assumed to be constant)
- \( t \) = time

2. **Nature of Acceleration in SHM**: In SHM, the acceleration is not constant. Instead, it is given by:
\[ a = -\omega^2 x \]
where \( \omega \) is the angular frequency and \( x \) is the displacement from the mean position. This means that the acceleration depends on the displacement \( x \).

3. **Dependence on Displacement**: Since the acceleration in SHM varies with displacement, it is not a constant value. As \( x \) changes, \( a \) changes accordingly. This is a key characteristic of SHM.

4. **Conclusion**: Because the equation \( v = u + at \) requires a constant acceleration, and since the acceleration in SHM is variable (dependent on \( x \)), we conclude that this equation cannot be used in the context of Simple Harmonic Motion.

### Final Answer:
No, we cannot use the equation \( v = u + at \) in Simple Harmonic Motion because the acceleration is not constant; it varies with displacement.