Question

Given a differential equation of SHM :

$a\frac{d^{2}x}{d{t}^2}+bx=0$

The time period of this oscillation is given by :

• A. $\frac{2\pi }{\sqrt{b}}$
• B. $2\pi \sqrt{b}$
• C. $2\pi \sqrt{b/a}$
• D. $2\pi \sqrt{a/b}$

Answer 1

The correct option is D $2\pi \sqrt{a/b}$

The given differential equation of SHM is:

$a\frac{d^{2}x}{d{t}^2}+bx=0$

Dividing whole equation by $a$, we have:

$\frac{d^{2}x}{d{t}^2}+\frac{b}{a}x=0$

Now compare it with the standard differential equation of SHM i.e. $\frac{d^{2}x}{d{t}^2}+{\omega }^{2}x=0$, we have

${\omega }^2=\frac{b}{a}\Rightarrow \omega =\sqrt{\frac{b}{a}}\Rightarrow \frac{2\pi }{T}=\sqrt{\frac{b}{a}}\Rightarrow T=2\pi \sqrt{\frac{a}{b}}$