Arrive an expression for time period of simple pendulum.

Explanation

The tangential component of force mg is `mg sin theta.`
Torque : - L `(mg sin theta)=Ialpha`
Angular acceleration `alpha=(-mgL sin theta)/(I)`
For smaller displacement `sin theta0^(@)=theta" (rad)"`
`"i.e. "alpha=(-mgLtheta)/(I) or omega=sqrt((mgL)/(I))` but `omega=(2pi)/(T) and I=mL^(2)`.
`(2pi)/(T)=sqrt((mgL)/(mL^(2)))" "therefore T=2pi sqrt((L)/(g))`.