Question

The differential equation representing the SHM of a particule is $\frac{9d^{2}y}{d{t}^2}+4Y=0.$The time period of the particle is fiven by

• A. $\frac{\pi }{3}sec$
• B. $\pi sec$
• C. $\frac{2\pi }{3}sec$
• D. $3\pi sec$

Answer 1

The correct option is D $3\pi sec$

The differential equation of S.H.M is

$9\frac{d^{2}y}{d{t}^2}+4y=0$

$9a+4y=0$ ($a=\frac{d^{2}x}{d{t}^2}$)

$a=-\frac{4}{9}x$

${\omega }^2=\frac{4}{9}$ ($a=-{\omega }^{2}x$)

$\omega =\frac{2}{3}$

$\frac{2\pi }{T}=\frac{2}{3}$

$T=3\pi$

The correct option is D.