Can we consider $\omega$ (angular frequency) in equation of simple harmonic motion (SHM) as the angular velocity of the object in circular motion, when we see simple harmonic motion as projection of circular motion?

  • $\begingroup$ Short answer: yes, but if and only if the circular motion is uniform circular motion $\endgroup$ – Eagle May 13 '19 at 20:48
  • $\begingroup$ Then if it's correct, it means angular frequency w=2pie/T should be equal to angular velocity w=v/r of the particle executing shm $\endgroup$ – Nikhil Pant May 13 '19 at 20:56
  • $\begingroup$ Yes, you're right. $\endgroup$ – Eagle May 13 '19 at 21:06
  • $\begingroup$ Have you learned about rotations in phase space? $\endgroup$ – Cosmas Zachos May 13 '19 at 22:09
  • $\begingroup$ In fact, this explains why the harmonic motion is sinusoidal, but not along any other periodic function. $\endgroup$ – safesphere May 14 '19 at 6:39

Oscillation as projection

Yes. The point on the circle with radius $R$ revolves around the centre, with angular velocity:


The projection on the RHS axis, call it $y$, is:

$$y(t)=R\sin(\omega t+\phi)$$

where $\phi$ is the angle $\theta$ at $t=0$.

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  • $\begingroup$ but do u really think the ω in (ω=θ) is equal to the ω in (y(t)=Rsin(ωt+ϕ)). basically my Que is can we really think the angular frequency in a shm as angular velocity of the object when we manipulate the motion as the shadow projection of circular motion (the the object is moving in a circular motion) $\endgroup$ – Nikhil Pant May 14 '19 at 8:01
  • $\begingroup$ Please note: $\omega=\dot{\theta}=\frac{\mathbf{d}\theta}{\mathbf{dt}}$ $\endgroup$ – Gert May 14 '19 at 14:22
  • $\begingroup$ It's more an analogy. But mathematically the projection of the position vector (red) of a particle moving uniformly on a circle onto any axis corresponds exactly to the description of an SHO. $\endgroup$ – Gert May 14 '19 at 14:32

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