A spring of negligible mass having a force constant k extends by an amount y when a mass m is hung from it. The mass is pulled down a little and released. The system begins to execute simple harmonic motion of amplitude A and angular frequency ω. The total energy of the mass-spring system will be


Correct option is


Let L be the relaxed length of the spring and y the extension produced in it due to force mg so that 

                ky = mg                                          …(i)

The displacement of the mass during oscillation is given by


At the instant when the displacement is x



Taking gravitational PE at the mean position to be zero, 

Gravitational PE at x = – mg x                                       … (v)

Adding (iii), (iv) and (v), we get 

Total energy of mass-spring system 






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