# Pendulum Using Lagrange And Hamilton

1. Oct 9, 2004

### skrao

i have been given a problem involving a pendulum, where its support point is accelerating vertically upward. The period of the pendulum is required. Anybody have any idea how to start this one? is it not just 2pi(L/g-a)^1/2?

Last edited: Oct 9, 2004
2. Oct 9, 2004

### PICsmith

First thing to do is write x, y and x', y' in terms of r and theta (polar coords). Draw a picture to help you visualize, then find the kinetic and potential energies and be sure to take into account the upwards acceleration, so you have both gravity and this upwards accelration acting on the mass. Then find the Lagrangian and/or Hamiltonian and use one of them to find the equations of motion.

3. Oct 10, 2004

### MiGUi

The period of a pendulum is not $$\nu = 2\pi \sqrt{\frac{L}{g}}$$ that is only an approximation to the right expression, which we can't solve exactly

Last edited: Oct 10, 2004
4. Oct 10, 2004

### reilly

skrao -- Ask yourself what the period would be if the upward acceleration was equal to g?

Regards,
reilly Atkinson