Question

Derive an expression for the velocity of a particle performing linear SHM using differential equation. Hence, find the expression for the maximum velocity.

Answer 1

$\frac{d^{2}x}{dl}+w^{2}x=0$

$\Rightarrow x=A\sin \left(wt+\varphi \right)$

differentiate with respect to $t$

$\Rightarrow \frac{dx}{dt}=Aw\cos \left(wt+\varphi \right)$

$\Rightarrow v=Aw\left\{\cos \left(wt+\varphi \right)\right\}$

$\therefore v_{max}=Aw$ (where $A$ is amplitude of medium)