Modeling Oscillating Systems: Physics Component Introduction

When any mechanical system is disturbed, within certain elastic limits, the resulting behavior is called simple harmonic motion. Some obvious examples include the behavior of pendulums, vibrating springs, diving boards, and tuning forks. Less obviously this motion shows up in a range of events from earthquakes to the vibration of atoms. Simple harmonic motion is characterized by periodic change in which the acceleration vector of an object is constantly changing, always directed toward its equilibrium position, and directly proportional to its displacement from equilibrium. Further, even as the amplitude of vibration decreases over time, the period of vibration remains constant.

Since the motion is periodic, the object repeatedly moves through a to-and-fro cycle of change always being pulled back towards its equilibrium position by a restoring force. A restoring force is common to any oscillating system, and depends upon particular elastic properties of the material that is vibrating.

Depending on the complexity of the oscillating system the students will build Stella models of simple oscillating systems or work with pre-built models. The students will analyze the components of the graphical output that relate to the corresponding behavior in the physical systems they have experimentally explored, such as frequency, period, wavelength and amplitude. Mathematically, a simple oscillating system can be modeled as a trigonometric function. Depending on the individual mathematical capability of the students, they can use various computational tools to further explore and analyze the sine wave representation of the oscillating systems.

It is especially important for the students to compare their experimental data with data obtained through modeling activities, thus reinforcing the viability of using computational tools for effective and reliable scientific exploration.