Large Amplitude Pendulums
Large Amplitude Pendulums
Without the small-angle approximation the differential equation is not the simple harmonic motion equation and the period is not independent of the amplitude. The exact period can't be written in simple closed form, but it can be written as an elliptic integral of the first kind (which can be numerically approximated) or written as a power series expansion. Short of that, various other approximations are also available. Plot one or two of the approximations you learn about below on the same graph as your experimental data.- The Large Angle Pendulum Period by Millet, TPT, March 2003
- A Simple Formula for the Large-Angle Pendulum Period by Kidd and Fogg, TPT, February 2002
- An accurate formula for the period of a simple pendulum oscillating beyond the small angle regime by Lima and Arun, AJP, Oct 2006
- Large-Angle Motion of A Simple Pendulum Physics 258/259, 2005
- Approximations for the period of the simple-pendulum based on the arithmetic-geometric mean by Carvalhaes and Suppes, AJP, December 2008
- Approximation expressions for the large-angle period of a simple pendulum revisited by Amrani and Beaudin, Rev, Mex, Fis. June 2008
- Comment on 'Approximation for a large-angle simple pendulum period' by Yuan and Ding, Eur. J. Phys., L79-L82, 2009
- Reply to 'Comment on "Approximation for a large-angle simple pendulum period"' by Belendez, Rodes, Belendez, Hernandez, Eur. J. Phys., L83-L86, 2009
- An approximate expression for the large angle period of a simple pendulum by Parwani, Eur. J. Phys, 37-39, 2004
- Series expression for exact period from Wikipedia Pendulum_(mathematics)
- Infinite series for exact period from Wikipedia Pendulum
- The Simple Pendulum Lab by James Parks at Univ Tenn
- The Simple Pendulum Lab at Youngstown State Univ
- Period Calculator at Hyperphysics
- Physics Notes on Pendulum Period at MIT, May 2009