# Pendulum and spinning mass -- Coupled

## Homework Statement

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.

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## The Attempt at a Solution

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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?

## Answers and Replies

Bystander
Science Advisor
Homework Helper
Gold Member
If we assume the length of the pendulum arm to be constant, it seems that the two masses are no longer coupled.
You have nailed it.