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

Answer

`40J`

Explanation

`m=2kg, T=4sec`
`T=2pi (sqrt(m/k))`
`rarr 2=2pisqrt(2/k)`
`rarr 2=pi(sqrt(2/k)`
`rarr 4=pi^2(2/k)`
`rarr k=(2pi^2)/4`
`=pi^2/2=5N/m`
but we know that
`F=mg=kx`
` rarr x=(mg)/k=(2xx10)/5=4`
:. Potential energy `=1(1/2)kx^2=1/2xx5xx16`

= `40J`