To demonstrate how a variable stiffness can be effectively used to stabilize vibrations, we will first present the example of
the controlled oscillator.
We consider the system depicted in Fig. 2. The simple harmonic oscillator, composed of a mass m and a spring of stiffness
k, is supported with a suspension system with a controlled stiffness of u and a fixed damping c. By introducing the state
vector x^ ¼ ½x^ 1; x^ 2
T and the matrices