A particle executing simple harmonic motion along a straight line. The velocity of the particle is `5ms^(-1)`, when it is at a distance of 4 m from mean position and `3ms^(-1)`, when at a distance of 9 m from mean position. Calculate the time taken by the particle to travel 3 m from the positive extremity of oscillation.

Explanation

To solve the problem, we need to determine the time taken by a particle executing simple harmonic motion (SHM) to travel 3 meters from the positive extremity of oscillation. We will use the information given about the particle's velocity at different positions to find the amplitude and angular frequency, and then calculate the time taken.

### Step-by-Step Solution:

1. **Identify Given Information:**
- Velocity \( V_1 = 5 \, \text{m/s} \) at position \( x_1 = 4 \, \text{m} \)
- Velocity \( V_2 = 3 \, \text{m/s} \) at position \( x_2 = 9 \, \text{m} \)

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