Question

The motion of a particle varies with time according to the relation y=a(sinωt + cosωt)

• A. The motion of oscillatory but not SHM.
• B. The motion is SHM with amplitude a.
• C. The motion is SHM with amplitude a√2.
• D. The motion is SHM with amplitude 2a.

Answer 1

Answer: (C)

The motion is SHM with amplitude a√2.

Answer 2

y = a (sinωt + cosωt)

=$A\sqrt{2}\left\{ \frac{1}{\sqrt{2}}\sin\omega t + \frac{1}{\sqrt{2}}\cos\omega t \right\}$

= a$\sqrt{2}$sin$\left( \omega t + \frac{\pi}{4} \right)$

∴ The motion is S.H.M. in nature and has an amplitude a√2.