When two displacements represented by y _ 1 = asin ( ) and y _ 2 =...

${y}_{1} = asin \omegat$

${y}_{2} = bcos \omegat = bsin \left(\omegat + \dfrac{\pi}{2}\right)$

Amplitude $A = \sqrt{{a}^{2} + {b}^{2} + 2abcos \dfrac{\pi}{2}}$

$A = \sqrt{{a}^{2} + {b}^{2}}$

Since the frequency for both motion are same, then the resultant motion will be SHM.