Question

For a particle in SHM, if the amplitude of displacement is $a$ and the amplitude of velocity is $v$ , then what will be the amplitude of acceleration?

• A. $va$
• B. $\frac{v^2}{a}$
• C. $\frac{v^2}{2a}$
• D. $\frac{v}{a}$

Answer 1

Answer: (B)

The equation for position of a particle under SHM, $x=asin\left(\omega t\right)$ ,
$\Rightarrow v=a\omega cos\left(\omega t\right)$ ,
maximum velocity, $v=\omega a$
$\text{Acceleration}=-a{\left(\omega \right)}^{2}sin\left(\omega t\right)$ ,
maximum acceleration, $f={\left(\omega \right)}^{2}a\Rightarrow f={\left(\frac{v}{a}\right)}^{2}a\Rightarrow f=\frac{v^2}{a}$