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Q.
A $10\,kg$ metal block is attached to a spring of spring constant $1000 \, nm^{-1}$. A block is displaced from equilibrium position by $10\,cm$ and released. The maximum acceleration of the block is
We know that spring does SHM
So, the restoring force is proportional to displacement
i.e., $F=-m \omega^{2} y$...(i)
$F=-k y$...(ii)
where $k=$ force constant of the spring
$m=10\, kg$
$A=10\, cm =0.1\, m$
Comparing the both equation, we get
$\omega^{2}=\frac{k}{m}$
$\Rightarrow \omega =\sqrt{\frac{k}{m}}= \sqrt{\frac{1000}{10}}$
$=10\, rad / s$
and acceleration in SHM
$a_{\max }=-\omega^{2} \cdot y$
where $\omega^{2}$ is constant
$=-10^{2} \times(0.1)=-10 m / s ^{2}=10\, ms ^{-2}$