# Dynamics/Solving Ordinary Differential Equations

< Dynamics

## Introduction[edit | edit source]

In dynamics and control, 2nd-order ordinary differential equations of a single variable are very common. For example, you may recall arguably the most famous example for a mass-spring-damper system given by the following:

- ,

where , , and describe the displacement, velocity, and acceleration of a system with a moving mass , damping coefficient , and a spring coefficient .

To cast this system in the form of a state-space model/representation that involves a series of 1st-order differential equations