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  4. The composition of two simple harmonic motions of equal periods at right angle to each other and with a phase difference of π results in the displacement of the particle along

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Q. The composition of two simple harmonic motions of equal periods at right angle to each other and with a phase difference of $\pi$ results in the displacement of the particle along

AIPMTAIPMT 1990Oscillations

Solution:

$x=a \sin \omega t$
and $y=b \sin (\omega t+\pi)=-b \sin \omega t$.
or $ \frac{x}{a}=-\frac{y}{b}$ or $y=-\frac{b}{a} x$
It is an equation of a straight line