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A body of mass 2 kg suspended through a ...

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.

Text Solution

Verified by Experts

The correct Answer is:
`40J`
`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`
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