The harmonic oscillator, with all its manifestations, is an extensively studied system. It possesses a single degree of freedom. More complicated systems have more degrees of freedom, for example, two pendulums connected by a spring. In such cases, the behaviour of each variable influences the other which leads to a coupling between the individual degrees of freedom. Energy can toggle between the two degrees of freedom. A well-known example is the Wilberforce pendulum, where the oscillation alternates between the longitudinal stretching of a vertical spring and the rotation of a cylindrical object hung at the end of that spring. The aim of this experiment is to investigate the dynamics of the Wilberforce pendulum.
|Software Code||Phystrack (Download)|
|Sample Results||Vertical oscillations for various moments of inertiaFourier contents for various moments of inertiaSquare of difference of squares of normal modes versus inverse of moments of inertia|
|Hardware Manual||Machining dimensions of the oscillating mass|
Further Readings and References
- Ch15 Oscillations Introduction to Physics , R. Resnick, D. Halliday, K. S. Krane , 5 390-413 , (2001).
- Wiberforce pendulum oscillations and normal modes American Journal of Physics , Richard E. Berg and Todd S. Marshall , 59 32-38 , (1991).
- The Pendulum: A Case Study in Physics Oxford University Press , Gregory L. Baker, James A. Blackburn 8-16 , (2005).