Question

The angle made by the string of a simple pendulum with the vertical depends on time as $\theta =\frac{\pi }{90}sin\left[\right(\pi s^{-1\left)t\right].}$ Find the length of the pendulum if $g={\pi }^{2}m{s}^{-2}.$

Answer 1

From the equation,

$\theta =\left(\frac{\pi }{0}\right)sin\left[\pi \right(se{c}^{-1}\left)t\right]$

$\therefore \omega =\pi se{c}^{-1}$

(Comparing with the equation of SHM)

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

$\Rightarrow T=2sec$

We know that, $t=2\pi \sqrt{\left(\frac{l}{g}\right)}$

$\Rightarrow 2=2\pi \sqrt{\left(\frac{l}{g}\right)}$

$\Rightarrow 1=\pi \sqrt{\left(\frac{l}{g}\right)}$

$\Rightarrow l=1m$

$\therefore$ Length of the pendulum is 1 m.