"Fine Structure" of the Simple Harmonic Oscillator

The Simple Harmonic Oscillator {SHO} is one of the most well known and commonly used theoretical models and experimental systems in physics. The basic properties of the SHO are widely discussed in physics books at all levels. However, in recent studies in my lab, several SHO systems manifested a number of consistent features beyond the simple behavior commonly expected. Although the systems still obey the simple SHO rules, these features are a "fine structure" of the basic system. The features involve relationships between resonant frequency, amplitude of oscillation at resonance, drive amplitude, sweep rate and even direction of sweep. Through a series of experiments and the design and construction of new "oscillators" we will study these features in as much detail as possible.

Participation in this project obviously requires abundant data acquisition but also may include designing and constructing experimental oscillators, testing and calibrating such devices, working with vacuum systems, working at lower temperatures (down to 77K), building and troubleshooting electronic circuits used to operate the oscillators, and working with theoretical models to explain the features we studied in the lab.

Coupled Harmonic Oscillators

Coupling implies that the behavior of one system is affected by the behavior of another. In this project we will connect two oscillators in such a way that their motions are coupled. In other words, the motion of each oscillator is affected by the motion of the other. A very famous, and perhaps familiar, case of such coupling is the Wilberforce pendulum. We will first construct prototypes of the coupled system in order to determine the best design features and the general behavior of such a system. From there the study really depends on what we find. One hopeful path is to consider this mechanical system to be a macroscopic example of spin coupling, as occurs in paired electrons. Again, data acquisition, design, construction, vacuum systems, low temperatures, electronics and machine shop work are all part of the overall project.