The particle is executing SHM on a line 4 cm long. If its velocity at mean position is 12 m/s , then determine its frequency.

Explanation

To solve the problem, we need to determine the frequency of a particle executing simple harmonic motion (SHM) given the length of the line (which is twice the amplitude) and the velocity at the mean position.

### Step-by-Step Solution:

1. **Identify the Amplitude (A)**:
The total length of the line is given as 4 cm. In SHM, this length represents the distance from the maximum negative displacement to the maximum positive displacement. Therefore, the amplitude \( A \) is half of this length:
\[
A = \frac{4 \text{ cm}}{2} = 2 \text{ cm} = 0.02 \text{ m}
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