Question

The average acceleration of a particle performing $SHM$ over one complete oscillation is

• A. $\frac{{\omega }^{2}A}{2}$
• B. $\frac{{\omega }^{2}A}{\sqrt{2}}$
• C. $zero$
• D. $A{\omega }^2$

Answer 1

The correct option is C $zero$

Let the SHM have the form $x=Asin(\omega t+\varphi )$

$⟹$ acceleration is of the form $a=-{\omega }^{2}Asin(\omega t+\varphi )$

Thus the average value of the acceleration=$\frac{-{\int }_0^{2\pi /\omega }{\omega }^{2}Asin(\omega t+\varphi )dt}{2\pi /\omega }=0$