Question

The equation of motion of a particle executing simple harmonic motion is $a+16{\pi }^{2}x=0$. In this equation, $a$ is the linear acceleration (in ${\text{m/s}}^2$) of the particle at a displacement $x$ (in meter). The time period in simple harmonic motion is

• A. $\frac{1}{4}\text{sec}$
• B. $\frac{1}{2}\text{sec}$
• C. $1\text{sec}$
• D. $2\text{sec}$

Answer 1

The correct option is B $\frac{1}{2}\text{sec}$

$a=-16{\pi }^{2}x$
Standard equation of SHM is:
$a=-{\omega }^{2}x$
Hence, comparing two equations, we get $\omega =4\pi$
and $T=\frac{2\pi }{\omega }=\frac{2\pi }{4\pi }=\frac{1}{2}\text{sec}$