S.H.M. Energy 


Simple Harmonic Motion, Energy 

 A mass on a spring transforms energy back and forth between kinetic and potential energy. If there were no dissipation, conservation of energy would dictate that the motion would continue forever. For any real vibrating object, the implication of the conservation of energy principle is that the vibrator will continue the transformation from kinetic to potential energy until all the energy is transferred into some other form. To set the object into motion, a net external force must do work on the mass to initially stretch the spring, that amount of work being 2 joules in the example below.

Graphic and definition provided by HyperPhysics

 E = KE + U

E = total energy 

KE = kinetic Energy 

U = potential energy 

m = mass 

ω = natural frequency 

A = amplitude 

t = time

 φ = phase shift

U = potential energy

x = distance from equilibrium