A) not a simple harmonic
B) simple harmonic with amplitude \[\frac{a}{b}\]
C) simple harmonic with amplitude \[\sqrt{{{a}^{2}}+{{b}^{2}}}\]
D) simple harmonic with amplitude \[\frac{(a+b)}{2}\]
Correct Answer: C
Solution :
Given, \[{{y}_{1}}=a\sin \omega t\] \[{{y}_{2}}=b\,\cos \omega t=b\sin \left( \omega t+\frac{\pi }{2} \right)\] The resultant displacement is given by \[y={{y}_{1}}+{{y}_{2}}=\sqrt{{{a}^{2}}+{{b}^{2}}}\sin (\omega t+\phi )\] Hence, the motion of superimposed wave is simple harmonic with amplitude \[\sqrt{{{a}^{2}}+{{b}^{2}}}.\]
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