Question

The angle made by the string of a simple pendulum with the vertical depends on time as θ=π90 sin [(π s-1)t]. Find the length of the pendulum if g = π2 m−2.

Answer 1

The length of the pendulum is $l=1 \mathrm{m}$

Explanation:

• The length of the pendulum can be derived from the equation $T=2 \pi \sqrt{\frac{l}{g}}.$We know that the angle made by the simple pendulum with the vertical direction is  $\theta=\left(\frac{\pi}{90}\right) \sin \left[\pi\left(s^{-1}\right) t\right]$.  
• Thus, on comparing the above equation with the equation of simple harmonic motion, we get  $\omega=\pi s^{-1}=2 s$.
• Therefore, the time period is $T=2 s$.  Hence, on substituting the known values, $2=2 \pi \sqrt{\frac{l}{\pi^{2}}}$ where l is the length of the pendulum. Solving the above equation, we get length of the pendulum $l=1 \mathrm{m}$.