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Homework Statement:

(1) By just looking at the time period of the oscillation, can we know whether the motion is simple harmonic or not? How?
(2) Is the same true for angular (circular) SHM?
Homework Equations:

A simple harmonic motion is described by:
##\dfrac{d^2 x}{dt^2}=\omega^2\ x##
For angular:
##\dfrac{d^2 \theta}{dt^2}=\omega^2\ \theta##
I am reading "Coulomb and the evolution of physics and engineering in eighteenthcentury France". There it is said in page 152 para 1 that "Coulomb found that within a very wide range, the torsion device oscillated in SHM".
My questions are:
(1) By just looking at the time period of the oscillation, how can we know whether the motion is simple harmonic or not?
(2) Is the same true for angular (circular) SHM?
My questions are:
(1) By just looking at the time period of the oscillation, how can we know whether the motion is simple harmonic or not?
(2) Is the same true for angular (circular) SHM?