Question

The displacement of a particle in simple harmonic motion in one time period is:

• A. $A$
• B. $2A$
• C. $4A$
• D. Zero

Answer 1

The correct option is D Zero

Let position of the particle at any instant $y=Asin(wt+\varphi )$

$y=Asin[\frac{2\pi }{T}t+\varphi ]$ where $w=\frac{2\pi }{T}$

Position of the particle after one time period $y_T=Asin[\frac{2\pi }{T}(t+T)+\varphi ]$

$y_T=Asin[\frac{2\pi }{T}t+2\pi +\varphi ]$

$⟹$ $y_T=Asin[\frac{2\pi }{T}t+\varphi ]$

Thus net displacement of the particle in one time period $s=y_T-y=0$