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!

  • $\begingroup$ 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. $\endgroup$ – David Z Oct 21 '11 at 6:48
  • $\begingroup$ 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! $\endgroup$ – Ben Elgar Oct 21 '11 at 7:16
  • $\begingroup$ 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. $\endgroup$ – David Z Oct 21 '11 at 7:23

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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