A block is resting on a piston which executes simple harmonic motion with a period $2.0 \,s$. The maximum velocity of the piston, at an amplitude just sufficient for the block to separate from the piston is .......... $ms ^{-1}$
Medium
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(b)
Period $(T)=2 \,s$
$\omega=\frac{2 \pi}{2}=\pi \,rad / s$
When block just represent from a piston, maximum acceleration must be equal to $g$.
$g=-\omega^2 x$
Acceleration is maximum when $x=A$
$g=-\omega^2 A$
or $A=\frac{9.8}{\pi^2}$
Maximum velocity $=A \omega$
$=\frac{9.8}{\pi^2} \times \pi$
$=\frac{9.8}{\pi} \,m / s$
$=3.119 \,m / s =3.12 \,m / s$
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