# Applications of overdamping, critical damping and underdamping

I am a math lecturer and in my teaching of second-order linear differential equations I present, as an application, the classical mass-spring-dashpot system (and its RLC analogue). According to my understanding, if the overdamping case modelled an automobile suspension system, the ride would be uncomfortable. Furthermore, critical damping represents the minimum damping that can be applied to the physical system without causing oscillation.

One textbook I use (Ordinary Differential Equations and Applications by Weighfer and Lindsay) says: (Critical damping) is often the desired configuration for practical aplications since it represents the weakest damping before oscillatory becomes possible.

Nevertheless, another textbook I use (Differential Equations for Engineers by Xie) states that: Most engineering structures fall in this category (i.e. underdamping case) with (the dimensionless) damping coeffient $$\zeta$$ usually less than $$10\%$$. [$$\zeta=\frac{\gamma}{2\sqrt{mk}}$$ for the mechanical system; $$\zeta=\frac{2}{R}\sqrt{\frac{C}{L}}$$ for the electrical analogue].

Question 1: Which author is right?

Question 2: In general What are some practical applications where each case (heavy, critical and light damping) is desirable or not desirable?

Thank you very much.

• If a car shock fails then it is underdamped and oscillates uncomfortably and dangerously. Why would overdamped be uncomfortable? Usually they bounce rebound and recover. Nov 20, 2022 at 14:30