Linear simple harmonic motion is a projection | vedclass

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(A) Linear simple harmonic motion $(SHM)$ is the projection of uniform circular motion $(UCM)$ on a diameter. In $UCM$,the particle experiences a cons

Vedclass · Accepted Answer

Yes,the forces involved are different.

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(A) Linear simple harmonic motion $(SHM)$ is the projection of uniform circular motion $(UCM)$ on a diameter. In $UCM$,the particle experiences a constant centripetal force $F_c = \frac{mv^2}{r} = m\omega^2r$ directed towards the center. In linear $SHM$,the particle experiences a restoring force $F = -m\omega^2x$,which is proportional to the displacement $x$ from the mean position and directed towards it. While the kinematics (position,velocity,acceleration) of the projection match $SHM$,the physical nature of the forces is different: $UCM$ requires a constant magnitude force,whereas $SHM$ requires a force that varies linearly with displacement.

Linear simple harmonic motion is a projection of uniform circular motion along any one diameter of a circle. Is there any distinction between these two?

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