Kinetic energy of SHM particle
`K(t) =(1)/(2) kA^(2) sin^(2) (omega t+phi)`
Potential energy `U(t) = kA^(2) cos^(2) (omega t+phi)`
Mechanical energy `E= K(t) +U(t)`
`therefore (1)/(2) kA^(2) [sin^(2) (omega t+ phi)+cos^(2)(omega t +phi)]`
`therefore E= (1)/(2)kA^(2)`.
Here, in table values of kinetic, potential and total energy in terms of period of SHM particle is shown and by using these values a graph of a energy versus time is shown.
Following points are clear from this graph : (1) In SHM both kinetic and potential energy are positive hence total energy is also positive.
(2) In SHM, kinetic energy becomes two time maximum in every period and becomes two times zero. This maximum kinetic energy is equal to the total energy.
(3) In SHM, potential energy becomes two times maximum in every period and become two time zero. This maximum potential energy is eaual to the total energy.
(4) The increase or decrease in kinetic energy from energy time of `(T)/(4)` in SHM is equal to decrease or increase in potential respectively.
(5) At any time the sum of kinetic and potential energy is constant and it is mechanical energy. Hence mechanical energy does not depend on time.
