question_answer 42)

                  A body is performing S.H.M. Then its                 (a) average total energy per cycle is equal to its maximum kinetic energy.                 (b) average kinetic energy per cycle is equal to half of its maximum kinetic energy.                 (c) mean velocity over a complete cycle is equal to \[\frac{2}{\pi }\] times of its maximum velocity.                 (d) root mean square velocity is \[\frac{1}{\sqrt{2}}\] times of its maximum velocities.

Answer:

                  (a, b, d) Total energy \[=\frac{1}{2}\,k{{r}^{2}}\,=\] maximum K.E.                 Average K.E. \[=\frac{1}{4}\,k{{r}^{2}}\]