Imagine two masses connected to each other by a string. One mass sits atop a table, while the other mass dangles below the table, as the string is fed through a hole in the center. The configuration looks like this: http://tuhsphysics.ttsd.k12.or.us/Tutorial/NewIBPS/PS5_3/5-32.JPG. Now push the swinging pass so that it start oscillating as a pendulum, and simultaneously push the top mass so that it starts moving in a circular motion. Assume the length of the pendulum arm is constant. Write the lagrangian and find the equations of motion.
The Attempt at a Solution
My confusion is this: If we assume the length of the pendulum arm to be constant, it seems that the two masses are no longer coupled. Thus the problem immediately reduces to a simple pendulum and a mass spinning with constant angular velocity. This doesn't seem correct. How am I supposed to interpret this problem so that the string never slides anywhere, yet the two masses are still coupled in some way?