Question

how to measure the potential energy in a compressed spring. here the formula m.g.h cannot work. so how to find it?

Answer 1

PE = mgh , only valids when we have work against gravity to lift it to a certain height say h , but for spring potential energy is 1/2 kx² , where k is spring constant & x is the distance , through which it is stretched

Answer 2

Measure the compression of the spring x.  that is the displacement x of the free moving end of the spring in compressed state.

Measure the spring constant k of the spring.  This can be known by suspending a known weight m  and measuring the extension x in spring.  k = F/x = m g / x.

The potential energy of the compressed spring: 1/2 k x²

Remember it is the Elastic potential energy of stored in the spring.

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If the mass is suspended vertically by a spring, then the mass block comes down by height h and is extended by h.  We assume that spring is massless.

Then conservation of energy tells:    m g h = 1/2 k x²