Question

A coical pendulum consists of a string of length `L` whose upper end is fixed and another end is tied to a bob. The bob is moving in horizontal circle with constant angular speed `omega` such that the string makes a constant angle `theta` with the verticle. calculate time period `T_(0)` of revolution of bob in terms of `L,g` and `theta`.

Answer 1

Time period of revolution `T-(0)=(2pi)/(omega)`
`T cos theta=mgimpliesT=(mg)/(cos theta)`
`T sin theta=m omega^(2)r`
`(mg)/(cos theta)sin theta =m omega^(2)L sin theta(since sin theta=(r )/(L))`
`omega^(2)=(g)/(L cos theta)impliesomega=sqrt((g)/(L cos theta))`
Time period `T_(0)=(2pi)/(omega)=2pisqrt((L cos theta)/(g))`