# Average kinetic energy of harmonic oscillator

1. Apr 30, 2015

### shanepitts

I was wondering why the average kinetic energy is calculated in this manner.

They are dividing the kinetic energy function by the period (noted here as To) and integrating it with limits from 0→To. Why?

(This is a tiny portion of a larger textbook example, not an actual assignment.)

Sorry for my ignorance of the basicalities of averages and integration.

2. Apr 30, 2015

### x86

I think that its because they are using the average value calculus identity.

That is, the average value of f from a to b is 1/(b-a) integral{ f(x) dx } from a to b

So it stands to reason that the average value from 0 to T_0 is 1/T_0 \integral ( K(t) dt ) from 0 to T_0

3. Apr 30, 2015

Thanks