Question

Show that the total energy of the particle performing linear S.H.M. is constant.

Answer 1

Consider a particle of mass ‘m’ which is performing linear S.H.M. of amplitude ‘a’ along straight line AB, with the centre O.  Let the position of the particle at some instant be at C, at a distance x from O.

Thus the kinetic energy of the particle performing linear S.H.M. and at a dis the ance of x1 from mean given by

Answer 2

Dear Student,

◆ Answer -

T.E. = 1/2 kA²

● Explanation -

For a particle performing linear S.H.M.,

P.E. = 1/2 kx²

K.E. = 1/2 k(A²-x²)

Total energy of a particle performing linear S.H.M. is sum of P.E. and K.E.

T.E. = P.E. + K.E.

T.E. = 1/2 kx² + 1/2 k(A²-x²)

T.E. = 1/2 k (x²+A²-x²)

T.E. = 1/2 kA²

As k and A are constant for in particular SHM, total energy will also be constant.

Thanks dear. Hope this helps you..