Mode Shapes for Multiple Degree-of-Freedom Oscillators

Whiffle baseballs and rubber bands are used to create a mass-spring system with 1, 2, 3, and 4 degrees-of-freedom. Each system is driven at its resonance frequencies, and the natural modes of vibration are demonstrated. The number of masses (different discrete objects undergoing displacement from equilibrium) determines the number of natural frequencies and mode shapes. As the number of degrees-of-freedom increases, the mode shapes begin looking like the mode shapes for a vibrating string fixed at both ends. Please check out www.acs.psu.edu/drussell/Demos... for animations of a computer model of this system.
Video was filmed at 240 fps using a Casio EX-FH20 digital camera.
Thanks to graduate student Matthew Shaw for helping setup the demonstration and for holding down the blue background in the wind for the last several clips.

[@unstuckchuck]

Thanks for taking the time to create this video - it really helped me understand the real-life meaning of "modes" in my system dynamics and vibrations course.

[@DanRussellPSU]

yes. In the graduate course "Fundamentals of Acoustics" that I teach at Penn State we work out the theory for the mode shapes and frequencies for an N-dof system. At my website (see link in the description above) I have a animations that I created in Mathematica from the mathematical model for 1,2,3,4-dof systems.

[@MoizuddinFarooq]

Amazing work there. Such a good demonstration. Explains the concept clearly well. I would really like to know the specifications of the motor involved .

[@jahirmiya733]

thank you....clears my visualization, very helpful indeed.

[@pop4ti]

Thank you for this amazing demonstration. I was wondering how to get the number of modes of vibrations for a five storey shear building have in 3D space. Thank you in advance.

[@berndeinfeldt1228]

Thanks for the reply, which I missed. I looked at the limit for a non-linear wave equation and found that the result differ, depending on the assumption made about the atomic structure of the string; i.e. if it is assumed that the string consist of discrete oscillators (atoms) or if it is a differentiable string. Currently looking for some (crow) funding to turn the notes (over hundred handwritten pages) and my old dissertation into a publication - difficult if you don´t live in the US.

[@peppyDa2nd]

This is interesting. I wonder if it could be applied to architecture.

[@berndeinfeldt1228]

Nice movie, did you work out the mathematical solution for a arbitrary finite number of masses?