https://rootloc.us/tags/dynamical-systems/ Recent content in Dynamical Systems on rootloc.us Hugo -- gohugo.io en-us © FL https://rootloc.us/posts/mass_spring_damper_101/ Mon, 01 Jan 0001 00:00:00 +0000 https://rootloc.us/posts/mass_spring_damper_101/ The model of the Mass-Spring-Damper system is a very simple (and yet useful) one. It can be used to understand a lot of concepts in Dynamical Systems, and to model more complex systems (like car suspensions) in a pretty accurate way. According to Newton’s second law we can write the equation of forces in this way: $$ m\textbf{a}=\Sigma \textbf{F} $$ The acceleration is the second derivative of our state variable x(t), $\Sigma \textbf{F}$ is the sum of the elastic force imposed by the linear spring (Hooke’s law), the viscous damping force imposed by the linear damper and the input force u(t).