Question

A body of mass $2kg$ suspended through a vertical spring executes simple harmonic motion of period $4s$. If the oscillations are stopped and the body hangs in equilibrium, find the potential energy stored in the spring.

Answer 1

Given mass= 2 kg and time period fro simple harmonic motion= 4 s.

We know Time period T of mass m on a spring of spring constant 'k'$=2\pi \sqrt{\frac{m}{k}}$

$T=2\pi \sqrt{\frac{m}{k}}k=\frac{4{\pi }^{2}m}{16}=4.93N$

ALso Force$=mass\times accelerationduegravity=kx$ -----1

where x is the displacement

Also potential energy of the spring is given as

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

Now from 1

x $\frac{2\times 10}{4.93}=4.05m$

Thus potential enrgy stored in the spring

$=\frac{1}{2}(4.93\times {4.05}^2)=40.43J$