Simple Harmonic Motion (1 Viewer)

[xwrathbringerx]

Hi could someone please show me how to do this???
Show that for any particle moving in simple harmonic motion, the ratio of the average over one oscillation to the max. speed is 2: pi.

 

[shaon0]

Hi could someone please show me how to do this???
Show that for any particle moving in simple harmonic motion, the ratio of the average over one oscillation to the max. speed is 2: pi.

x=Asin(nt+K)+B
x'=Ancos(nt+K)
x"=-An^2.sin(nt+K)
Max speed occurs at x"=0 ie. t=-K/n.
x'=An.cos(0)=An.
Thus, max speed is An.
Time for 1 osscillation is: T=2pi/n
v=s/t => v=4A/(2pi/n) => v=2An/pi
At max speed: An:2An/pi
1:2/pi => 2 : pi ratio