Question

The equation of motion of a particle executing SHM is $\left(\frac{d^{2}x}{d{t}^2}\right)+kx=0$. The time period of the particle will be ?

• A. $\frac{2\pi }{\sqrt{k}}$
• B. $2\pi$
• C. $2\pi k$
• D. $2\pi \sqrt{k}$

Answer 1

The correct option is A $\frac{2\pi }{\sqrt{k}}$

The equation of motion,

$\frac{d^{2}x}{d{t}^2}+kx=0$

$a=-kx$

${\omega }^2=k$ ($a=-{\omega }^{2}x$)

$\omega =\sqrt{k}$

$\frac{2\pi }{T}=\sqrt{k}$

Time period,

$T=\frac{2\pi }{\sqrt{k}}$

The correct option is A.