Question

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

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

Answer 1

Answer: (A)

The correct option is D $3\pi sec$
The differential equation representing S.H.M of a particle is,

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

$9a+4y=0$

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

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

$\omega =\sqrt{\frac{4}{9}}=\frac{2}{3}$

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

$T=3\pi sec$

The correct option is D.