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The average kinetic energy in one time period is equal to average potential energy in that period but they are not same in interval. How ?
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The average kinetic energy in one time period is equal to average pote...
Take a mass-attached-to-spring case as an example. We know the frequency is related to spring constant by k=mk=mω^2
The elastic potential energy is kx^2/2 where xx is the displacement from the spring’s equilibrium position taken at x=0x=0.
In simple harmonic motion, x=Asin(ωt)x=Asin(ωt)where AA is the amplitude.
Plug this in and integrate over one period. Use the property that average of the square of sines over 1 period is equal to half. Therefore you have UU =(1/4)kA2=(1/4)kA^2
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