How to Find the Lagrangian for a Simple Pendulum with Moving Support?

[Reshma]

Find the Lagrangian for a simple pendulum of mass m whose point of support moves uniformly on a vertical circle with constant frequency $\omega$ in a uniform gravitational field.

Let 'l' be the length of the pendulum string. Using plane polar coordinates:
Let T be the KE of the pendulum.
$$T = {1\over 2}m \left(\dot {r}^2 + r^2\dot{\theta}^2\right)$$
Let V be the PE.
$$V = -mgr\cos \theta$$
r = l = constant
I am wondering how to add the angular velocity $\omega$ to the equation of motion. Need help here.

 

[JohanL]

how is omega related to theta?

 

[OlderDan]

Find the Lagrangian for a simple pendulum of mass m whose point of support moves uniformly on a vertical circle with constant frequency $\omega$ in a uniform gravitational field.

Let 'l' be the length of the pendulum string. Using plane polar coordinates:
Let T be the KE of the pendulum.
$$T = {1\over 2}m \left(\dot {r}^2 + r^2\dot{\theta}^2\right)$$
Let V be the PE.
$$V = -mgr\cos \theta$$
r = l = constant
I am wondering how to add the angular velocity $\omega$ to the equation of motion. Need help here.

As with your other problem, You need to pick a pair of coordinates. A pair of angles looks good here also.