Jen is working on a spring–mass–damper system, as shown in Fig. P7–68. She remembers from her dynamic systems class that the damping ratio ζ is a nondimensional property of such systems and that ζ is a function of spring constant k, mass m, and damping coefficient c. Unfortunately, she does not recall the exact form of the equation for ζ. However, she is taking a fluid mechanics class and decides to use her newly acquired knowledge about dimensional analysis to recall the form of the equation. Help Jen develop the equation for ζ using the method of repeating variables, showing all of your work.

FIGURE P7–68

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//////// //// Spring (k) Damper (c) Mass (m)