A particle moves simple harmonically in a straight line starting from rest. In first 't' sec it travels a distance 'a' and in next 't'sec it travels '2a' in same direction. Then its time period is ?

Explanation

To solve the problem step by step, we will analyze the motion of the particle in simple harmonic motion (SHM) and derive the time period based on the given distances traveled in specified time intervals.

### Step 1: Understanding the Motion
The particle starts from rest, which means it is at the extreme position of its motion. In SHM, the particle's position can be described by the equation:
\[ y(t) = A \cos(\omega t) \]
where \( A \) is the amplitude, and \( \omega \) is the angular frequency.

### Step 2: Analyze the First Time Interval
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