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While this question seems similar to Is uniform circular motion an SHM, the answers there appear to contradict Berg & Stork (2004).

Berg & Stork first state that simple harmonic motion (SHM) requires a linear restoring force. And that's apparent with things like a pendulum or a mass on a spring. However, they then describe uniform circular motion as SHM even when there's no restoring force, e.g., a mathematical point moving uniformly in a circle. So is the restoring force not really a requirement for SHM? Is all that's needed to call it SHM the fact that you can describe its motion with a sine wave (which you can do for either x or y in uniform circular motion)?

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  • $\begingroup$ "However, uniform circular motion is also described as SHM even when there's no restoring force." Citation, please. $\endgroup$
    – Chemomechanics
    Jul 18 at 20:16
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    $\begingroup$ Does this answer your question? Is uniform circular motion an SHM? $\endgroup$
    – Chemomechanics
    Jul 18 at 20:17
  • $\begingroup$ "Citation, please" ... I saw in "The Physics of Sound" by Berg & Stork, 3rd ed., ,p. 6: "Uniform circular motion, viewed from a distant point in the plane of the motion, is SHM...." True, it doesn't actually say "no restoring force," but the discussion refers to just a point moving in a circle (not a physical object with a central force). $\endgroup$
    – Matt
    Jul 18 at 22:17
  • $\begingroup$ Thank you. Agreed that the projection of UCM on a perpendicular plane is indistinguishable from SHM. $\endgroup$
    – Chemomechanics
    Jul 18 at 22:44

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In the role of the "restoring force" there is the cartesian component of the centripetal force. The whole force causes the body to move in circle, the component causes the cartesian coordinate to change as sine function of time.

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