# Energy in SHM

A particle executing SHM possesses two types of energy: potential energy and kinetic energy.

# Potential energy

Potential energy is an account of the displacement of the particle from its mean position. The restoring force

*F*= â€“*ky*against which work has to be done.So

*Important Points*- Potential energy maximum and equal to total energy at extreme positions
*y*= Â±*a*;*Ï‰t*=*Ï€*/2;*t*=*T*/4 - Potential energy is minimum at mean position,
*U*_{min}= 0, when*y*= 0;*Ï‰t*= 0;*t*= 0

# Kinetic energy

Kinetic energy is because of the velocity of the particle.

Kinetic energy,

- Kinetic energy is maximum at mean position and equal to total energy at mean position.

â€‹ when

*y*= 0;*t*= 0;*Ï‰**t*= 0- Kinetic energy is minimum at extreme position.

*K*

_{min}= 0, when

*y*=

*a*;

*t*=

*T*/4,

*Ï‰t*=

*Ï€*/2;

# Total energy

Total mechanical energy = Kinetic energy + Potential energy

*E*=

Total energy is not a position function, i.e., it always remains constant.

# Energy position graph

Kinetic energy (

*K*)Potential Energy (

*U*) =Total energy (

*E*) =It is clear from Fig. 2 that

**Fig. 2**

- Kinetic energy is maximum at mean position and minimum at extreme position.
- Potential energy is maximum at extreme position and minimum at mean position.
- Total energy always remains constant.

**Kinetic energy**

**Potential energy**

where

*Ï‰**â€™*= 2*Ï‰*and , i.e., in SHM, kinetic energy and potential energy vary periodically with double the frequency of SHM (i.e., with time period*T**â€™*=*T*/2).From Fig. 3, we note that potential energy or kinetic energy completes two vibrations in a time during which SHM completes one vibration. Thus, the frequency of potential energy or kinetic energy is double than that of SHM.

**Fig. 3**