Question

Question #d2662

Answer 1

In Simple harmonic Motion of an ideal particle instantaneous mechanical energy is given by the expression

`"Mechanical Energy"E_m="Potential Energy"E_p+"Kinetic Energy"E_k`

At mean position
`"Potential Energy"=0`. Therefore all the energy is its
Kinetic energy`=E_k(max)`,
Similarly at extreme positions `"Kinetic Energy"=0`. Hence all the enrgy is its
`"Potential Energy"=E_p(max)`

The total mechanical energy remains constant instantaneously throughout the cycle. Therefore, total mechanical energy as it passes through a position that is 0.617 of the amplitude away from the equilibrium position is also equal to
`E_m(0.617)=E_p(max)=E_k(max)` ......(1)

To calculate actual value of total mechanical energy we need details of the Simple Harmonic Motion.

For example, if an ideal spring having spring constant `k` is stretched by a maximum length`=x_max`, its potential energy at extreme position is given as
`E_p(max)=1/2kx_max^2`
From equation (1) above
`E_m(0.617)=E_p(max)=1/2kx_max^2`