shm question (1 Viewer)

[saa]

need a bit of help with a shm question.. I'm posting it from what I remember when I saw it this arvo (don't have a copy of it with me now) so hopefully I get it right

Anyway, the equation was x = asinnt + bcosnt
And we were asked to find v and a which was easy
Then asked to find period and amplitude.

Period is 2pi/n
Amplitude is n * sqrt(a^2 + b^2)

The period and amplitude answers I got from the answers section but couldn't see how to get them, can anyone help? (especially the amplitude one!)

 

[wogboy]

Use the fact that:


a*sin@ + b*cos@
= sqrt(a^2 + b^2) * (sin@ * sinx + cos@ * cosx)
= sqrt(a^2 + b^2) * cos(@ - x)

where sinx = a/sqrt(a^2 + b^2)

 

[wogboy]

Amplitude is n * sqrt(a^2 + b^2)

Amplitude should be independent of n: Amplitude = sqrt(a^2 + b^2)
(for the position x, that is)

 

[saa]

Thanks for the quick reply..

Yeah, you'd be right about the amplitude, I was just going by memory..

I can see you've basically factorised out the sqrt(a^2 + b^2), but this bit I'm not sure on:

where sinx = a/sqrt(a^2 + b^2)

How?

And so you mean cosx = b/sqrt(a^2 + b^2) too?



Actually, just read another thread, and have you got it from the acceleration?