Question

A spring store $5J$ of energy when stretched by $25cm$. It is kept vertical with the lower end fixed. A block fastened to its other end is made to undergo small oscillation. If the block makes $5$ oscillation each second, what is the mass of the block?

Answer 1

$x=25cm=0.25m$

$E=5J$

$f=5$

So, $T=1/5sec$

Noe P.E. $=\left(1/2\right)k{x}^2$

$\Rightarrow \left(1/2\right)k{x}^2=5\Rightarrow \left(1/2\right)k(0.25{)}^2=5\Rightarrow k=160N/m$

Again, $T=2\pi \sqrt{\frac{m}{k}}\Rightarrow \frac{1}{5}=2\pi \sqrt{\frac{m}{160}}\Rightarrow m=0.16kg$.