Average energy mass on a spring

AI Thread Summary
To find the mean potential energy of a mass on a spring, the maximum potential energy is given by the formula 1/2*k*x0^2. The mean potential energy is indeed half of the maximum potential energy, but the calculation involves considering the potential energy at any instant, expressed as 1/2*k*x^2 = 1/2*k*x0^2*cos^2(ωt+ø). The average value of cos^2(ωt+ø) over a complete cycle is 1/2. Thus, the mean potential energy is confirmed to be half of the maximum potential energy.
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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.

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The Attempt at a Solution


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

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