Silva_physics
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Let <r> (t)/dt= 1/2Pi * Integrate[r(t)*dt,{r,t-Pi,t+Pi}] denote the running average of r over one cycle of the sinosoidal oscillation.
I have to show that d<r>/dt = <dr/dt>, it does not matter whether we differentiate or time-average first.
Should I work with Leibniz rule? Can I use some symmetry of interval, I don't really know, something I tried to do but not successfully.
Can anybody, please, show solution?
I have to show that d<r>/dt = <dr/dt>, it does not matter whether we differentiate or time-average first.
Should I work with Leibniz rule? Can I use some symmetry of interval, I don't really know, something I tried to do but not successfully.
Can anybody, please, show solution?