A system is oscillating with undamped simple harmonic motion. Then the This question has multiple correct options:A system is oscillating with undamped simple harmonic motion. Then the This question has multiple correct options:

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Average total energy per cycle of the motion is its maximum kinetic energy.

Average total energy per cycle of the motion is

times its maximum kinetic energy.

Root mean square velocity is

times its maximum velocity.

Mean velocity is

of maximum velocity.

answer is A.

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Detailed Solution

Concept- The average total energy of a system's undamped simple harmonic motion is equal to the sum of its kinetic and potential energy. We will use the angular velocity expression of this system to determine the link between stiffness and mass.
Total energy of system is

remains constant, when system is at mean position,

, and

. so the average of total energy is equal to total energy at the mean position which is maximum kinetic energy.
similarly, at extreme points,

and

.
so the average of total energy is equal to total energy at extreme position which is maximum potential energy.
Now, if

Maximum velocity is

and rms value of velocity is

rms value of

)
Hence, the correct answer is option 1,3.

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