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 ?

Explanation

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^2 theta - 2 sin^2 theta) = g cos theta`
Time period T=` 2pi sqrt((1)/(g cos theta))`