Spring-Mass-Damping System with Two Degrees of Freedom

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This Demonstration shows the dynamics of a spring-mass-damping system with two degrees of freedom under external forces. The motion of the system is represented by the positions and of the masses and at time . Both masses have a spring connected to a stationary base, with spring constants and ; also for the spring connecting the two masses. The motion of the masses is damped, with damping factors and ; also for damping between the two masses. The masses are acted upon by external forces and .


The Demonstration gives the solution of the differential equations from Newton's second law of motion, then shows free-body diagrams at the top of the graphic, with the natural frequencies of the system. The two plots at the bottom show the position and velocity of the two masses as functions of time.


Contributed by: Frederick Wu (November 2015)
Open content licensed under CC BY-NC-SA




[1] S. S. Rao, Mechanical Vibrations, 5th ed., Upper Saddle River, NJ: Prentice Hall, 2011 pp. 472–477.

[2] K. Ogata, System Dynamics, 4th ed., New York: Prentice Hall, 2004 pp. 453–458.

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