Question

For a particle exicuiting S.H.M. equation of motion is given by $\frac{d_{2}x}{d{t}^2}+4x=0$. Calculate the time period.

Answer 1

Th equation of motion for a particle executing S.H.M is given by

$\frac{d^{2}x}{d{t}^2}+4x=0$ . . . . . .(1)

we know that acceleration $a=\frac{d^{2}x}{d{t}^2}$

$a=-4x$

${\omega }^2=4$ ($a=-{\omega }^{2}x$)

$\omega =2$

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

The time period, $T=\pi sec$