Loading [MathJax]/extensions/TeX/boldsymbol.js
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\tp}{\thinspace .}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
Generalization: damping, nonlinear spring, and external excitation
mu'' + f(u') + s(u) = F(t),\quad u(0)=I,\ u'(0)=V,\ t\in (0,T]
Input data: m , f(u') , s(u) , F(t) , I , V , and T .
Typical choices of f and s :
- linear damping f(u')=bu , or
- quadratic damping f(u')=bu'|u'|
- linear spring s(u)=cu
- nonlinear spring s(u)\sim \sin(u) (pendulum)
