SHM can go SMD (1 Viewer)

[fullonoob]

Show that for any particle moving in SHM, the ratio of the average speed over one oscillation to the max speed is 2 : pi.

 

[hscishard]

"SMH can go SMD"

Get in line buddy.

 

[fullonoob]

i was first in line bro

 

[shaon0]

i was first in line bro

lol, i think i proved this a while ago. It's probs still on the 1st page of the MX1 forum.
EDIT: http://community.boredofstudies.org/13/mathematics-extension-1/245066/simple-harmonic-motion.html

 

[fullonoob]

nice proooo

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

on the line v = s /t
s = distance right, could you tell me how to get 4A please

 

[shaon0]

nice proooo

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

on the line v = s /t
s = distance right, could you tell me how to get 4A please

Go up till max, then go down again=2A; Keep going down till min then go back up again=2A.
So, 4A