Question

If an SHM is represented by $\frac{d^{2}x}{d{t}^2}+\alpha x=0$, then time period of the SHM is

• A. $2\pi \sqrt{\alpha }$
• B. $2\pi \alpha$
• C. $\frac{2\pi }{\sqrt{\alpha }}$
• D. $\frac{2\pi }{\alpha }$

Answer 1

The correct option is C $\frac{2\pi }{\sqrt{\alpha }}$

Equation of SHM,
$\frac{d^{2}x}{d{t}^2}+\alpha x=0$
Comparing the above equation with the general equation of SHM i.e
$\frac{d^{2}x}{d{t}^2}+{\omega }^{2}x=0$
${\omega }^2=\alpha$
$\Rightarrow \omega =\sqrt{\alpha }$
Since time period, $t=\frac{2\pi }{\omega }=\frac{2\pi }{\sqrt{\alpha }}$