A particle of mass 2 kg executing SHM has amplitude 10 cm and time period is 1 s.Find (i) the angular frequency (ii) the maximum speed (ii) the maximum acceleration (iv) the maximum restoring force (v) the speed when the displacement from the mean position is 8 cm (vi) the speed after `(1)/(12)` s the particle was at the extreme position (vii) the time taken by the particle to go directly from its mean position to half the amplitude (viii) the time taken by the particle to go directly from its exterme position to half the amplitude.

Explanation

Let's solve the problem step by step.

### Given:
- Mass of the particle, \( m = 2 \, \text{kg} \)
- Amplitude, \( A = 10 \, \text{cm} = 0.1 \, \text{m} \)
- Time period, \( T = 1 \, \text{s} \)

### (i) Find the angular frequency \( \omega \):
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