Jen is working on a spring-mass-damper system, as shown in

Chapter 7, Problem 69P

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Problem 69P

Jen is working on a spring-mass-damper system, as shown in Fig. P7-72. 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 constantk, 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. (Hint: Typical units for k are N/m and those for c are N ⋅ s/m.)