# Tag Archives: state space

## State Space Representation Of A Mass Spring Damper System

Hello,
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:

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

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]