A) The motion is oscillatory but not S.H.M.
B) The motion is S.H.M. with amplitude a
C) The motion is S.H.M. with amplitude \[a\sqrt{2}\]
D) The motion is S.H.M. with amplitude \[2a\]
Correct Answer: C
Solution :
\[y=a(\cos \omega \,t+\sin \omega \,t)\]\[=a\sqrt{2}\left[ \frac{1}{\sqrt{2}}\cos \omega \,t+\frac{1}{\sqrt{2}}\sin \omega \,t \right]\] \[=a\sqrt{2}[\sin 45{}^\circ \cos \omega \,t+\cos 45{}^\circ \sin \omega \,t]\] \[=a\sqrt{2}\sin (\omega \,t+45{}^\circ )\] Þ Amplitude \[=a\sqrt{2}\]
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