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

Answer 1

The correct option is A $\frac{\pi }{3}$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