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  • When will the motion of a simple pendulum be simple harmonic ?

When will the motion of a simple pendulum be simple harmonic?

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Let us consider a pendulum whose,

Length = l

Mass of bob = m, viz., displaced by angle = \theta

Now, Restoring force = F=-mg \sin \theta

Also, if \theta is small then

Sin \theta = \theta

  =\frac{arc}{radius}

  =\frac{x}{l}

Thus,

F=-mg\frac{x}{l}

OrF \propto (-x)           …………. (since m, g & l are constants)

Thus, simple harmonic for the small-angle

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infoexpert24

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