Question

A simple pendulum of length `l` is suspended from the celing of a cart which is sliding without friction on as inclined plane of inclination theta . What will be the time period of the pendulum?

Answer 1

Here , point of suspension has an acceleration .a=g`"sin"theta` (down the plane). Further, g can be resolved into two components `g"sin"theta` (along the plane) and `g "cos" theta` (perpendicular to plane).

`therefore g_("eff")=g " cos "theta` (perpendicular to plane)
`therefore T=2pisqrt((l)/(|g_("eff")|))=2pisqrt((l)/(g"cos"theta))`