Average kinetic energy of harmonic oscillator

[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 T_o) and integrating it with limits from 0→T_o. 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.

Thanks in advance

 

[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

 

[shanepitts]

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

Thanks