Question

The differential equation of all simple Harmonic motion of given period $\frac{2\pi }{n}$ is:

• A. $\frac{d^{2}x}{d{t}^2}+nx=0$
• B. $\frac{d^{2}x}{d{t}^2}+n^{2}x=0$
• C. $\frac{d^{2}x}{d{t}^2}-n^{2}x=0$
• D. $\frac{d^{2}x}{d{t}^2}-\frac{1}{n^2}x=0$

Answer 1

The correct option is B $\frac{d^{2}x}{d{t}^2}+n^{2}x=0$

Given $T=\frac{2\pi }{n}$
$\Rightarrow \frac{2\pi }{\omega }=\frac{2\pi }{n}$
$\Rightarrow \omega =n$
Equation $y=Asin\omega x$
$\Rightarrow y_1=\omega Acos\omega x$
$y_2=-w^{2}Asinwx$
$y_2+{\omega }^{2}y=0$
$\Rightarrow y_2+n^{2}y=0$