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  • Show that the motion of a particle represented by y = sin ax – cos cot is simple harmonic with a period of 2π/ω.

Show that the motion of a particle represented byy = \sin wt - \cos wt is simple harmonic with a period of \frac{2\pi}{\omega}.

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y = \sin \omega t - \cos \omega t

   = \sqrt{2}\ \left [sin \omega t \frac{1}{\sqrt{2}}- \cos \omega t \frac{1}{\sqrt{2}} \right ]

    = \sqrt{2}\ sin\left [ \omega t- \frac{\pi }{4} \right ]

Comparing this equation with standard SHM we get,

\omega = \frac{2 \pi }{T}

Or t = \frac{2 \pi }{\omega}

Posted by

infoexpert24

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