Alegbra of simple harmonic motion

[Clairepie]

Homework Statement

I am wanting to learn how to rearrange equations for simple harmonic motion equations (I am new to LaTeX so gimme a break!) mostly to find time (t) as the subject, but I am not very good at rearranging equations with sin/cos etc and want to get better at it, partly homework partly maths skills for the future, partly I like to learn anyway!

Homework Equations

$$a_{x} = -Aw^2 sin(wt)$$

$$1/sin(wt) = -Aw^2/a_{x}$$

As the initial phase = 0 it's not included here. and w= omega

The Attempt at a Solution

I know that
$$1/sin(wt) = -Aw^2/a_{x}$$

But not sure where to go from there.

Clairepie

 

[tiny-tim]

Hi Clairepie!

(have an omega: ω )

sinωt = a_x/Aω²

ωt = arcsin( a_x/Aω² )

t = arcsin( a_x/Aω² )/ω

 

[Clairepie]

Thank you and for the omega cheeky little ω!

 

[tiny-tim]

Yes, I've never noticed that before, ω does look cheeky, doesn't it …

either chipmunky-cheeky or non-specific rear-cheeky! ​

 

[Clairepie]

You mean it looks like a bum?! I can't unsee it now! I just ohpe I don't slip up in an exam "2 pi f = bum"

 

[Clairepie]

After 6pm I don't fix typos!