Show Energy Equality of Simple Pendulum with Equipartition

[Glenda]

Homework Statement

How would one show that the average total energy of a simple pendulum is equal to twice the average kinetic energy of the pendulum?

Homework Equations

E = T + V = 1/2 ml**2 (θ'**2) + mgl cos(θ)

The Attempt at a Solution

Maybe use equipartition?

 

[mfb]

Maybe use equipartition?

Then you have to show that your pendulum satisfies the assumptions going into that theorem. In particular, your pendulum is not in thermal equilibrium with anything, and a different potential shape will lead to a different result so it does not apply to all pendulum-like systems.

You can explicitly calculate the average kinetic energy by integrating over one period.