The Driven Mass and Spring Mesh model displays the dynamics of a 2D array of masses coupled by springs and driven by a sinusoidal force.  The model shows a time-dependent animation of the displacement or each mass.

The driving force can be applied at a single point (shown in red) or uniformly at all mesh points and the drive frequency f and amplitude A can be set as well as a damping coefficient b.  As the frequency is varied the mesh vibrates strongly (resonates) at some frequencies and very little at others. These resonances have patterns that were first studied by Ernst Chladni and this simulation is designed to investigate these patterns using an idealized mass and spring model.

In order to find the resonances, it is useful to plot the mechanical energy as a function of frequency f after the system reaches its oscillatory steady state.  A resonance scan option shows this plot.

The  Driven Mass and Spring Mesh model is a supplemental simulation for the article "Chladni Patterns on Drumheads: A Physics of Music Experiment" by Randy Worland in The Physics Teacher 49(1), 24-27 (2011) and has been approved by the authors and The Physics Teacher editor.  The model was developed using the Easy Java Simulations (EJS) modeling tool.  It is distributed as a ready-to-run (compiled) Java archive.  Double clicking the ejs_mech_DrivenMassAndSpringMesh.jar file will run the program if Java is installed.

Please note that this resource requires at least version 1.5 of Java.