Question

The equation of simple harmonic motion of a particle is $\frac{d^{2}x}{d{t}^2}+0.2\frac{dx}{dt}+36x=0$. Its time period is approximately

• A. $\frac{\pi }{6}\text{s}$
• B. $\frac{\pi }{4}\text{s}$
• C. $\frac{\pi }{3}\text{s}$
• D. $\frac{\pi }{2}\text{s}$

Answer 1

Answer: (C)

$\frac{\pi }{3}\text{s}$

The standard differential equation of SHM is
$\ddot{x}+{\omega }^{2}x=0$.
The coefficient of $x$ is always ${\omega }^2$.
Hence, we get ${\omega }^2=36$
$\omega =6$
$T=\frac{2\pi }{\omega }$
$T=\frac{\pi }{3}\text{s}$
Hence option C is correct.