- Force \(F(t)=m\,g-k\,(\|p(t)\|-l^0)\,\frac{p(t)}{\|p(t)\|}\;\;\), \(k\) spring stiffness, \(l^0\) rest length
- Second order differential equation: \(m\,p''(t)=mg-k\,(\|p(t)\|-l^0)\,\frac{p(t)}{\|p(t)\|}\)
- First order system \(\displaystyle \underbrace{\left(\begin{array}{c}p \\
v\end{array}\right)'(t)}_{u'(t)}=\underbrace{\left(\begin{array}{c}v(t) \\
g-k/m\,(\|p(t)\|-l^0)\,\frac{p(t)}{\|p(t)\|}\end{array}\right)}_{\mathcal{F}(u,t)}\)
