System Equations

Derivation of system equations is not always an easy task. This section covers some of the systems one is most likely to come across.

Spring Mass Damper system (unforced vibration): m*a + c*v + kx = 0

In Simulink or Simscape we can represent it in this way:

a = -c/m*v - k/mx

and this is the response

Spring Mass Damper system (forced vibration)

Using the differential equations using Laplace transform: Laplace2.pdf LaplaceTransformExamples

In Simulink we can represent it this way with 3 gains of 1/mass, Damping Coeff, Spring Stiffness:

Modelling Forced Vibration

Horizontal forced vibration system

Elevator