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I have two formulae:

Displacement = Amplitude * Cos(Angular Frequency * Time)

Velocity = - Amplitude * Angular Frequency * Sin(Angular Frequency * Time)


$x = Acos(wt)$

$v = -A.w.sin(wt)$

And the question is using these two formulae show $v = \pm W\sqrt{A^2 - x^2}$

Thanks for your help in advance!

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closed as off topic by David Z Oct 21 '11 at 6:46

Questions on Physics Stack Exchange are expected to relate to physics within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here.If this question can be reworded to fit the rules in the help center, please edit the question.

Hi Ben, welcome to Physics Stack Exchange! This is really a math question - or rather a math problem, since you haven't actually asked a question. It's not really about physics, though. Plus, it sounds a lot like a homework problem, and this is not a homework help site; we have a set of guidelines for asking questions of an educational nature, which require focusing on the concept that's giving you trouble, not just posting the question itself. – David Z Oct 21 '11 at 6:48
Sorry! You're right it was homework, albeit an extension question, but it was set by my physics teacher so I figured physics was the place to be. But thanks I'll read through the guidelines! – Ben Elgar Oct 21 '11 at 7:16
Thanks for understanding :-) As a general rule, basically you should "dig into" your problem at least enough to figure out whether it's the math or the physics that is really giving you trouble. – David Z Oct 21 '11 at 7:23
up vote 0 down vote accepted

Calculate $x^2 +\frac{v^2}{\omega ^2}$:

$x^2 + \frac{v^2}{\omega ^2}=A^2(cos^2(\omega t) + sin^2(\omega t) )$

$x^2+ \frac{v^2}{\omega ^2}=A^2$

$v^2=\omega ^2(-x^2 + A^2)$

Which gives us

$v=\pm \omega \sqrt{-x^2+A^2}$

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Thanks! That was very helpful! – Ben Elgar Oct 21 '11 at 7:17

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