Question

The position x of particle moving along x- axis varies with time t as x= A sin$\left(\omega t\right)$ where A and $\omega$ are positive constants. The acceleration a of particle varies with its position (x) as

• A. a=Ax
• B. a=$-{\omega }^{2}x$
• C. a=A$\omega x$
• D. a=${\omega }^{2}xA$

Answer 1

Answer: (B)

a=$-{\omega }^{2}x$

Given, $x=Asin\left(\omega t\right)$

$\Rightarrow v=A\omega cos\left(\omega t\right)$

$\Rightarrow a=-A{\omega }^{2}sin\left(\omega t\right)$ $\Rightarrow a=-{\omega }^{2}x$