When two displacements represented by $y_1 = asin\left( \omega t \right)$ and $y_2 = bcos\left(\omega t \right)$ are superimposed the motion is
AIPMT 2015, Medium
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Here, $y_{1}=a \sin \omega t$
$y_{2}=b \cos \omega t=b \sin \left(\omega t+\frac{\pi}{2}\right)$
$y_{2}=b \cos \omega t=b \sin \left(\omega t+\frac{\pi}{2}\right)$
Hence, resultant motion is $SHM$ with amplitude
$\sqrt{a^{2}+b^{2}}$.
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