A particle executes a simple harmonic motion of time period T. Find the time taken by the particle to go directly from its mean position to half the amplitude.

Explanation

To solve the problem of finding the time taken by a particle executing simple harmonic motion (SHM) to move from its mean position to half the amplitude, we can follow these steps:

### Step 1: Understand the Motion
In simple harmonic motion, the displacement \( x \) of the particle from the mean position can be described by the equation:
\[ x(t) = A \sin(\omega t) \]
where:
- \( A \) is the amplitude,
- \( \omega \) is the angular frequency, given by \( \omega = \frac{2\pi}{T} \) (with \( T \) being the time period).
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