Tag Archives: state space

State Space Representation Of A Mass Spring Damper System

I plan to write a bunch of posts about simulating dynamic systems using Python.
I will be using the mass-spring-damper (MSD) system as an example through those posts so here is a brief description of the typical MSD system in state space.

Mass-Spring-Damper System


Schematic of mass-spring-damper

The differential equation that describes a MSD is:

m \ddot{x} + c \dot{x} + k x = u

x : position of mass [m] at time t [s]
m : mass [kg]
c  : viscous damping coefficient [N s / m]
k  : spring constant [N / m]
u : force input [N]

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Filed under Dynamic Simulations using Python