Question

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

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

Answer 1

Answer: (B)

$x=A \sin \omega t$
$\frac{d x}{d t}=A \omega \cos \omega t$
$\Rightarrow \frac{d^{2} x}{d t^{2}}=-A \omega^{2} \sin \omega t$
$\Rightarrow a=-\omega^{2} x (\because A \sin \omega t=x)$