Answer to Question #127320 in Physics for Olabisi

Question

The period T of oscillation of a simple pendulum depends on the length L, and acceleration due to gravity g . Determine the exact form of dependence

Answer 1

The differential equation of oscillation of a simple pendulum

$\frac{d^2\theta}{dt^2}+\frac{g}{l}\sin\theta=0$

after solution

$T=2\pi\sqrt{\frac{l}{g}}\sum{((\frac{(2n)!}{(2^n\cdot n!)})^2\cdot \sin^{2n}\frac{\theta}{2})}.$