Question

The motion of a particle varies with time as $y=a(\sin \omega t+\cos \omega t)$, then

• 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
  2$a$

Answer 1

The correct option is C the motion is S.H.M. with amplitude $a\sqrt{2}$

$y=a(cos\omega t+sin\omega t)$
$=a\sqrt{2}\left(\frac{1}{\sqrt{2}}\cos \omega t+\frac{1}{\sqrt{2}}\sin \omega t\right]=a\sqrt{2}\left(\sin 45°\cos \omega t+\cos 45°\sin \omega t\right]=a\sqrt{2}\sin (\omega t+45°)Amplitude\left(A\right)=a\sqrt{2}$