Pendulum with Counterweight
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
A rod is supported in the middle (which is taken as the origin) and can turn freely. On one end of the rod there is a pivot with a pendulum attached to a red bob swinging from it. At the other end of the rod is a blue counterweight.
[more]
Contributed by: Erik Mahieu (October 2014)
Open content licensed under CC BY-NC-SA
Snapshots
Details
The system as described has two degrees of freedom: and are the angular displacements of the counterweight arm and the pendulum, with initial values and .
The rod length is and the counterweight has mass The pendulum has rod length and its bob has mass .
The potential energy of the system is .
The kinetic energy of the system is .
The resulting Lagrangian is and the equations of motion are
,
.
Permanent Citation