Spring-Mass System

When two physical elements are driven by a common force (yet have independent velocities, as we'll soon see is quite possible), they are formally in parallel. An example is a mass connected to a spring in which the driving force is applied to one end of the spring, and the mass is attached to the other end, as shown in Fig.7.11. The compression force on the spring is equal at all times to the rightward force on the mass. However, the spring compression velocity does not always equal the mass velocity . We do have that the sum of the mass velocity and spring compression velocity gives the velocity of the driving point, i.e., . Thus, in a parallel connection, forces are equal and velocities sum.

Figure 7.12 shows the electrical equivalent circuit corresponding to Fig.7.11.

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.