A simple pendulum of length `l` and mass `m` free to oscillate in vertical plane. A nail is located at a distance `d=l-a` vertically below the point of suspension of a simple pendulum. The pendulum bob is released from the position where the string makes an angle of `90^@` from vertical. Discuss the motion of the bob if (a) `l=2a` and (b) `l=2.5a`.

Explanation

To solve the problem, we will analyze the motion of a simple pendulum bob released from a vertical position (90 degrees from the vertical) and how it behaves when it encounters a nail located below the point of suspension. We will consider two cases based on the given lengths of the pendulum.

### Given:
- Length of pendulum: \( l \)
- Mass of pendulum bob: \( m \)
- Distance from the point of suspension to the nail: \( d = l - a \)

### Case (a): \( l = 2a \)
...