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Yes, but it involves a second order differential equation. Using the mass, spring constant and damping constant any physical object or assembly's damping ratio can be calculated. In the design of the vehicle the damping ratio was determined by the engineers at the automaker depending on the type of car. A sports car would have a higher damping ratio (maybe 0.7 or so) than a cushy luxury car. Over time the damping ratio will change as the components age. The most obvious is the bouncy feeling when you don't replace your struts or shocks as intended. That's when your tight sports car's suspension starts to behave like a 70's Buick. You just lowered your damping ratio without knowing it.

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Q: Calculation of damping ratio for car suspension?
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