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
AIPMT 1990, Medium
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(a) If ${y_1} = {a_1}\sin \omega \,t$ and ${y_2} = {a_2}\sin (\omega \,t + \pi )$
==> $\frac{{{y_1}}}{{{a_1}}} + \frac{{{y_2}}}{{{a_2}}} = 0$
==> $\frac{{{y_1}}}{{{a_1}}} + \frac{{{y_2}}}{{{a_2}}} = 0$
==> ${y_2} = - \frac{{{a_2}}}{{{a_1}}}{y_1}$
This is the equation of straight line.
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