Average energy mass on a spring

[thatguy14]

Homework Statement

Hi, I hope this isn't a silly question. I am looking to find the mean potential energy of a mass on a spring with spring constant k and maximum displacement x0.

Homework Equations

The Attempt at a Solution

I know the maximum energy is 1/2*kx0^2 so would the mean potential energy be half that?

 

[projjal]

Yes, the mean PE will be half of the maximum , but not just like that.
PE at any instant is 1/2 kx² = 1/2kx₀²cos²(ωt+ø) ,
avg. of cos²(ωt+ø) over a time period is 1/2.

 

[thatguy14]

ah okay thanks!