2n is the frequency ofkinetic energy and potential energy as 2 times both these comes max value in a full cycle

Frequency of Variation of Kinetic Energy in SHM

In Simple Harmonic Motion (SHM), the kinetic energy of the system varies periodically with time. The frequency of this variation can be determined based on the frequency of the SHM.

Understanding Simple Harmonic Motion (SHM)
SHM is a type of periodic motion where the restoring force acting on the system is directly proportional to the displacement of the system from its equilibrium position, and it always acts towards the equilibrium position. This type of motion can be observed in various physical systems, such as a mass-spring system or a pendulum.

Relationship between Kinetic Energy and SHM
In SHM, the total mechanical energy of the system remains constant since there is no dissipative force acting on it. The mechanical energy is the sum of the potential energy and the kinetic energy of the system. As the system oscillates, the potential energy is converted into kinetic energy and vice versa.

Frequency of Variation of Kinetic Energy
The frequency of the variation of kinetic energy in SHM is equal to the frequency of the motion itself. This means that the answer to the given question is (b) n.

Explanation:
- The frequency of SHM, denoted by 'n', is the number of complete oscillations per unit time. It represents the rate at which the system oscillates back and forth.
- Since kinetic energy is directly related to the motion of the system, it also varies with the same frequency 'n'.
- In each complete oscillation, the system goes through one complete cycle of converting potential energy to kinetic energy, and vice versa. This cycle repeats 'n' times in one second.
- Therefore, the kinetic energy of the system varies 'n' times per second, which is the same as the frequency of SHM.

Conclusion
The frequency of variation of kinetic energy in a SHM is equal to the frequency of the motion itself. Thus, the correct answer to the given question is (b) n.