The resultant of two rectangular simple harmonic motions of the same frequency and equal amplitudes but differing in phase by $\frac{\pi }{2}$ is
AIPMT 1997, Medium
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$x=a \sin \omega t$
$y=a \sin (\omega t+\pi / 2)=a \cos \omega t$
or, $\quad \frac{x}{y}=\frac{\sin \omega t}{\cos () t}=\tan \omega t$ or, $\frac{x}{y}=\frac{x}{\sqrt{a^{2}-x^{2}}},$
or, $y^{2}=a^{2}-x^{2}$ or, $x^{2}+y^{2}=a^{2}$.
It is an equation of a circle.
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