What is the time period of a pendulum on an inclined plane?

[Abhishekdas]

Period of a pendulum...

Homework Statement

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

Homework Equations

T=2(pi) root(l/g_eff)

The Attempt at a Solution

There is this concept of g_eff(g effective) which i don't know how to apply...So basically how to do this sum?

 

[abhishek ghos]

when the (pendulum + cart)system moves along the inclined plane, they do not feel the effect of any gravity in that direction as if they were in free fall in the sliding direction.
so, what remains is the g component perpendiculur to the slide direction, which is your effective g in this case.

 

[Abhishekdas]

Ya...that is okay...for this sum...but in general how to find the direction of g(eff)...
I mean for some general cases there must be some way to find the time period using the general method ...ie showing that the a=-w^2*x or torque=-w^2(theta) for the system and then using T=2(pi)/w... For other cases i have done it many times...even for a normal pendulum(the commom derivation)...But i am not getting such a method for tilted pendulums...