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I'm a bit confused about simple harmonic motion...

If a particle is in simple harmonic motion, to calculate the maximum velocity can I use either displacement = 0 or acceleration = 0, since i know in both graphs a zero in displacement and acceleration corresponds to maximum velocity?

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You're correct.

Physically, the maximum speed (velocity is a vector! Speed is its magnitude, which is what you're talking about) happens when the object that's moving passes by the origin and that is the point of zero displacement. It's also the point of zero acceleration because the restoring force behind the motion is zero at that point (and acceleration is force divided by mass).

Incidentally, the minimum speed happens at the opposite situation, namely, at the extreme ends of the motion. Since those are the extreme ends, the particle can't move beyond those and has to momentarily stop there (hence, zero speed). Those points are also where the acceleration is largest in magnitude, pulling the particle back towards the origin.

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  • $\begingroup$ @DavidQuinn Not very sportsman-like, David. Just because I pointed out that your answer was likely to confuse the OP is not a good reason to remove your answer and down-vote mine in retaliation. By down-voting it you may cause the OP to be left wanting for another answer when mine is correct and of good quality. We're all here to help people learn, no? $\endgroup$ – wltrup Aug 5 '15 at 9:07
  • $\begingroup$ I have removed my answer because it is clearly unsatisfactory. The problem I have with your answer is that it doesn't refer clearly to the properties or definition of SHM. Perhaps you could back up your statements with some equations? $\endgroup$ – David Quinn Aug 5 '15 at 12:08
  • $\begingroup$ "I have removed my answer because it is clearly unsatisfactory." - You didn't think so when we were arguing about it but I'm glad you recognise it now. "The problem I have with your answer is that it doesn't refer clearly to the properties or definition of SHM." - If you have a problem with my answer, then why did you down-vote it only after our disagreement over your answer and your decision to remove it? "Perhaps you could back up your statements with some equations?" - My answer is correct and complete, despite the lack of any equations. (cont.) $\endgroup$ – wltrup Aug 5 '15 at 17:46
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    $\begingroup$ (cont.) I explicitly chose not to write any equations to encourage Isabelle to develop an intuition for SHM since her question shows that to be missing. Spoon-feeding her a complete derivation wouldn't be half as useful. $\endgroup$ – wltrup Aug 5 '15 at 17:47

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