The vertical motion of a huge piston in a machine is approximately SHM. A block of 5 kg is placed on the piston. The maximum amplitude of the piston's SHM for the block and the piston to remains together is 0.99m. Find the frequency .
Hint `:` `v= (1)/( 2pi)sqrt((k)/(m))`
Find k
For maximum displacement ` x_(max) =A`
For maximum restoring force , `F= - kA = -mg`
`:. k= (mg)/( A)`. Put the valeu of K in `v =(1)/( 2pi ) sqrt((k)/(m))` to find v .

Explanation

To solve the problem step by step, we will follow the hints provided and the reasoning from the video transcript.

### Step 1: Identify the given values
- Mass of the block, \( m = 5 \, \text{kg} \)
- Maximum amplitude of the piston's SHM, \( A = 0.99 \, \text{m} \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \) (assuming standard value)

### Step 2: Find the spring constant \( k \)
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