Alegbra of simple harmonic motion

AI Thread Summary
The discussion focuses on rearranging equations related to simple harmonic motion, specifically to isolate time (t) in the equation a_{x} = -Aw^2 sin(wt). The user expresses difficulty with manipulating equations involving sine and cosine functions. A solution is provided, showing that t can be expressed as t = arcsin(ax/Aω²)/ω. The conversation includes light-hearted banter about the appearance of the Greek letter omega (ω). Overall, the thread emphasizes the importance of mastering equation rearrangement for both academic and personal growth in mathematics.
Clairepie
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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


<br /> a_{x} = -Aw^2 sin(wt) <br />

<br /> 1/sin(wt) = -Aw^2/a_{x}<br />

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

The Attempt at a Solution



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

But not sure where to go from there. :confused:

Clairepie
 
Last edited:
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Hi Clairepie! :smile:

(have an omega: ω :wink:)

sinωt = ax/Aω2

ωt = arcsin( ax/Aω2 )

t = arcsin( ax/Aω2 )/ω :smile:
 
Thank you and for the omega cheeky little ω!
 
Yes, I've never noticed that before, ω does look cheeky, doesn't it …

either chipmunky-cheeky or non-specific rear-cheeky! :biggrin:​
 
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"
 
After 6pm I don't fix typos!
 
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