A simple pendulum is suspended from the roof of a trolley that moves freely down a plane of inclination theta. What is the time period of oscillation ? What is the angle made by the string with the inclined plane in the mean position ?

A simple pendulum is suspended from the roof of a trolley that moves f

1.	A simple pendulum is suspended from the roof of a trolley that moves freely down a plane of inclination theta. What is the time period of oscillation ? What is the angle made by the string with the inclined plane in the mean position ?
Answer» Solution :The effective ACCELEATION g. is the RESULTANT of g acting VERTICALLY downwards and the inertial acceleration g `sin theta` acting up the PLANE. `g. = sqrt(g^2 + g^2 sin^2 theta + 2(g)(g sin theta) cos (90^@ +theta))` `=gsqrt(1+sin^2theta - 2 sin^2 theta) = g cos theta` Time PERIOD T=` 2pi sqrt((1)/(g cos theta))`