Question

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

Answer 1

$x=25cm=0.25m,E=5J,f=5$

So, $T=\frac{1}{5}sec.$

Now, $PE=\frac{1}{2}k{x}^2$

$\Rightarrow \frac{1}{2}k{x}^2=5$

$\Rightarrow \frac{1}{2}k(0.25{)}^2=5$

$k=160N/m$

Again $T=2\pi \sqrt{\left(\frac{m}{k}\right)}$

$\Rightarrow \frac{1}{5}=2\pi \sqrt{\left(\frac{m}{160}\right)}$

$\Rightarrow m=0.16kg$