A block is resting on a piston which is moving vertically with simple harmonic motion of period $1.0 s$. When the amplitude of motion  is A , the block and piston separates  and at this amplitude the maximum velocity of the piston is $v_m .$ Then

If $A$ be the amplitude of motion, then maximum acceleration,

$a={\omega }^{2}A$

The block will separate from the piston when the piston moves downwards, so $$\begin{gathered} mg – N = ma \\ \therefore N = m (g – a) \end{gathered}$$

To leave contract, $N=0$

$$\begin{gathered} \therefore a=g \\ or {\omega }^{2}A=g \\ \therefore A=\frac{g}{{\omega }^2}=\frac{g}{{\left(2\pi /1\right)}^2}=0.25 m \end{gathered}$$

Maximum velocity $v_{max}=\omega A =\left(\frac{2\pi }{1}\right)\times 0.25 m=1.57 m/s$