Question

When a block of mass m is suspended from the free end of a massless spring having force constant k, its length increases by y. Now when the block is slightly pulled downwards and released, it starts executing S.H.M with amplitude A and angular frequency ω. The total energy of the system comprising of the block and spring is ……..

(A) (1/2) mω² A²

(B) (1/2) mω² A² + (1/2) ky²

(C) (1/2) ky²

(D) (1/2) mω² A² – (1/2)ky²

Answer 1

 The correct option (B) (1/2) mω² A² + (1/2) ky²

Explanation:

When block of mass m is suspended from a spring having spring constant k, length increases by y.

∴ potential energy gained by spring = (1/2) ky²

when system executes SHM, energy gained by system = (1/2) mω² A²

∴ Total find energy of system = (1/2) mω² A² + (1/2) ky²