2f , Because in a time period (T) KE & PE two times minimum & two times maximum

Frequency of Variation of Kinetic and Potential Energy in SHM

In Simple Harmonic Motion (SHM), a particle oscillates back and forth about an equilibrium position, following a sinusoidal path. The frequency of SHM, denoted as 'f', represents the number of complete oscillations or cycles the particle completes per unit time. It is related to the time period (T) of the motion through the equation: f = 1/T.

Relationship between Kinetic Energy and Potential Energy in SHM

In SHM, the particle experiences a restoring force that is proportional to its displacement from the equilibrium position. As a result, the particle's total mechanical energy remains constant throughout the motion. This total mechanical energy is the sum of its kinetic energy (KE) and potential energy (PE).

Variation of Kinetic Energy in SHM

During SHM, the particle's displacement from the equilibrium position continuously changes. As the particle moves away from the equilibrium position, its velocity increases, resulting in an increase in kinetic energy. Conversely, as the particle moves towards the equilibrium position, its velocity decreases, leading to a decrease in kinetic energy.

The variation of kinetic energy is sinusoidal in nature and is out of phase with the displacement of the particle. The maximum kinetic energy occurs when the displacement is zero (at the equilibrium position), and the kinetic energy is minimum when the displacement is maximum.

Variation of Potential Energy in SHM

The potential energy of the particle in SHM is directly related to its displacement from the equilibrium position. As the particle moves away from the equilibrium position, its potential energy increases. Conversely, as the particle moves towards the equilibrium position, its potential energy decreases.

The variation of potential energy is also sinusoidal in nature and is in phase with the displacement of the particle. The maximum potential energy occurs when the displacement is maximum, and the potential energy is minimum when the displacement is zero (at the equilibrium position).

Frequency of Variation of Kinetic and Potential Energy

Since the variation of kinetic and potential energy in SHM is sinusoidal, their frequencies of variation are equal to the frequency of SHM, denoted as 'f'. This means that the kinetic and potential energy undergo complete cycles or oscillations with the same frequency as the particle's oscillations.

The phase relationship between the variation of kinetic and potential energy depends on the initial conditions of the motion. However, their frequencies remain the same throughout the motion.

In summary, in SHM, the frequency of variation of both kinetic and potential energy is equal to the frequency of the motion, denoted as 'f'. The kinetic energy varies sinusoidally and is out of phase with the displacement, while the potential energy also varies sinusoidally but is in phase with the displacement.