Particle Simple harmonic motion particle problem

[<3Science]

Homework Statement

For a particle in simple harmonic motion, show that vmax = (pi/2) vaverage, where vaverage is the average speed during one cycle of the motion.

Homework Equations

v(t) = -vmaxsin(wt + phi)
vmax = 2piA/ T = wA

The Attempt at a Solution

I'm really not sure at all how to start this, but I am guessing there really wouldn't be a numerical value just theory based?

 

[collinsmark]

I'm really not sure at all how to start this, but I am guessing there really wouldn't be a numerical value just theory based?

Normally I would insist that show more of your efforts first, but this one gave me a little trouble at the beginning too.

To start with, determine the average speed over one period. The only tricky part is figuring out what "average speed" really means. The average velocity is zero, so that certainly doesn't help. It's also not the root mean square (rms) velocity. Don't go that way.

To find the average speed, first determine the total distance the object travels in one period (not to be confused with displacement). It's a simple function of the amplitude A in,
x = Acos(ωt + Φ). But don't over-think it. How many As are traversed during a single period? Once you have the total distance, divide that by the period T. That's the average speed.