Partition between kinetic and potential energy?

[M_1]

Hi,

If I have a body which is freely vibrating with kinetic energy given by, say,
E_kin=(1-1/10sin(ωt))cos²(ωt)

what can be said about the potential energy? Of course the total energy should be constant but how big is it, in other words what is the potential energy?

Thanks!

 

[UltrafastPED]

The potential energy of the vibrating body is its elastic energy. If the body is in a gravity well a complete analysis would include the gravitational potential, but this would appear as a damping force on the vibrations in most cases.

A quantitative approach would be to find the maximum value for the kinetic energy; this will occur when the potential energy is minimized. This would be the total energy of the system.

 

[Nugatory]

Hi,

If I have a body which is freely vibrating with kinetic energy given by, say,
E_kin=(1-1/10sin(ωt))cos²(ωt)

what can be said about the potential energy? Of course the total energy should be constant but how big is it, in other words what is the potential energy?

Asking what the potential energy is is like asking how high something is: The answer depends on the arbitrary choice of a zero point, so we might say that an object is 2 meters off the floor, or 8 meters above ground level, or 123 meters above sea level, and they'd all be just as right.

Here we have ##E_{tot}=E_{kin}+E_{pot}##, so the potential energy is ##E_{pot}=E_{tot}-E_{kin}##, and we are free to choose any value for E_{tot} that we want, as long as we're consistent. It's often convenient to choose ##E_{tot}## so that ##E_{pot}## is zero when ##E_{kin}## is at a maximum.