A body undergoing simple harmonic motion has a maximum acceleration of 8 m`//s^(2)` , and a maximum speed of`1.6 m//s`. Find the period and the amplitude of the motion.

Explanation

To solve the problem, we need to find the period and the amplitude of a body undergoing simple harmonic motion (SHM) given its maximum acceleration and maximum speed.

### Given Data:
- Maximum acceleration, \( a_{\text{max}} = 8 \, \text{m/s}^2 \)
- Maximum speed, \( v_{\text{max}} = 1.6 \, \text{m/s} \)

### Step 1: Relate Maximum Acceleration and Maximum Speed to Amplitude and Period
In SHM, the maximum acceleration \( a_{\text{max}} \) and maximum speed \( v_{\text{max}} \) are related to the amplitude \( A \) and the angular frequency \( \omega \) by the following equations:
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