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If a body of mass m suspended by a sprin...

If a body of mass m suspended by a spring comes to rest after a downward displacement `y_(0)` find
(a) the force constant of the spring,
(b) loss in gravitational potential energy and
(c) gain in elastic potential energy.

Text Solution

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(a) For equilibrium
`ky_(0)=mg`
i.e, `k=mg//y_(0)`
(b) As the mass m has descended a distance `y_(0)` loss in potential energy `=mgy_(0)`
(c) As the spring is stretched by `y_(0)`
gain in elastic energy `=1/2ky_(0)^(2)=1/2mgy_(0)`
[as from Eqn. (a)`k=(mg)/y_(0)`]
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