Page - 258 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python 3.6, Volume Second Edition

258 8 SolvingOrdinaryDifferentialEquations Fig. 8.28 General oscillating system Fig. 8.29 A pendulum with forces Thisequation is,however,morecommonlyreordered to mu′′+f(u′)+s(u)=F(t). (8.66) Because the differential equation is of second order, due to the term u′′, we need two initial conditions: u(0)=U0, u′(0)=V0 . (8.67)