Physics Help Forum Is uniform circular motion an example of SHM?
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 Jun 3rd 2018, 12:49 AM #1 Junior Member   Join Date: May 2018 Posts: 11 Is uniform circular motion an example of SHM? I realise a projection of an object doing UCM appears as SHM, but does UCM object meet the criteria of a type of SHM? Thanks
 Jun 3rd 2018, 01:22 AM #2 Senior Member   Join Date: Apr 2017 Posts: 484 From search ... Definition of simple harmonic motion. : a harmonic motion of constant amplitude in which the acceleration is proportional and oppositely directed to the displacement of the body from a position of equilibrium : the projection on any diameter of a point in uniform motion around a circle. From that definition is seems UCM is not SHM.... the projection is not the same as the motion
Jun 3rd 2018, 02:30 AM   #3
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 Is uniform circular motion an example of SHM? -------------------------------------------------------------------------------- I realise a projection of an object doing UCM appears as SHM, but does UCM object meet the criteria of a type of SHM? Thanks

Of course not.

Just think about the two forms of motion.

Depending where you start from

SHM
The velocity magnitude rises to a maximum and then decreases to zero, whereupon it reverses direction.
The acceleration, over the same track, decreases to zero, then increases to a maximum then reverses direction.

CM
The velocity has constant magnitude, but the direction constantly changes, but it never reverses or drops to zero.
The acceleration has constant magnitude but the direction constantly changes, but never reverses or drops to zero.

In fact CM can be considered as the vector sum of two orthogonal SHM motions, which is why the projections are effectively vector components on two orthogonal axes.

Jun 6th 2018, 06:53 PM   #4
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 Originally Posted by justme I realise a projection of an object doing UCM appears as SHM, but does UCM object meet the criteria of a type of SHM? Thanks
I agree with studiot. No. But the projection does as you mentioned. See:
http://www.newenglandphysics.org/other/French_shm.pdf

Last edited by Pmb; Jun 6th 2018 at 07:17 PM.

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