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A particle executes SHM with amplitude A...

A particle executes SHM with amplitude `A` and angular frequency `omega`. At an instant the particle is at a distance `A//5` from the mean position and is moving away from it. Find the time after which it will come back to this position again and also find the time after which it will pass through the mean position.

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To solve the problem, we will follow these steps: ### Step 1: Determine the angle θ The particle is at a distance \( \frac{A}{5} \) from the mean position. We can find the angle \( \theta \) using the cosine function: \[ \cos(\theta) = \frac{x}{A} = \frac{\frac{A}{5}}{A} = \frac{1}{5} \] Thus, ...
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