The vertical motion of a huge piston in a machine is approximately SHM with a frequency of 1Hz.A block of mass 20 kg is placed on the piston . What is the maximum amplitude of the piston's SHM for the block and the piston to remain together .
Hint `:` `v= (1)/( 2pi)sqrt((k)/(m))`
Find k
For maximum displacement ` x_(max) =A`
For maximum restoring force , `F= - kA = -mg`
`:. A = (mg)/(k) = (mg) /( momega^(2))= (g)/( omega^(2))`

Explanation

To solve the problem, we will follow the steps outlined in the video transcript and derive the maximum amplitude of the piston's simple harmonic motion (SHM) for the block and the piston to remain together.

### Step-by-Step Solution:

1. **Identify Given Values**:
- Frequency of SHM, \( f = 1 \, \text{Hz} \)
- Mass of the block, \( m = 20 \, \text{kg} \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \) (approximately)
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