Initial population.

1 files changed, 52 insertions, 0 deletions

diff --git a/src/input/damped.input.pamphlet b/src/input/damped.input.pamphlet
new file mode 100644
index 00000000..4e0e5310
--- /dev/null
+++ b/src/input/damped.input.pamphlet
@@ -0,0 +1,52 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input damped.input}
+\author{The Axiom Team}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{License}
+<<license>>=
+--Copyright The Numerical Algorithms Group Limited 1994.
+@
+<<*>>=
+<<license>>
+-- Input file to solve linear second order differential equations
+-- with driving force A*cos(wt).
+
+-- The equation is solved at y(0)=y'(0)=0 for 
+--    (i)   an overdamped, forced motion example  c**2-4*k*m > 0
+--    (ii)  critically damped                     c**2-4*k*m = 0
+--    (iii) underdamped                           c**2-4*k*m < 0
+
+-- The resulting equations are then plotted.
+
+)clear all
+y := operator y
+deq := m*D(y x, x, 2) + c*D(y x, x) + k*(y x) = A * cos (w * x)
+
+solve(deq, y, x=0, [0,0])                     -- takes a few minutes
+ex:=%
+eval(%, [c=6,k=5,m=1,A=6*sqrt(5),w=sqrt(5)])  -- c**2-4*k*m = 16
+draw(%,x=0..15,title=="Overdamping")
+
+eval(ex, [k=5,m=1,A=6*sqrt(5),w=sqrt(5)])     -- c**2-4*k*m = 0
+limit(%,c=sqrt(20),"right")                   -- otherwise division by zero
+draw(%,x=0..15,title=="Critically Damped")
+
+eval(ex, [c=2,k=5,m=1,A=6*sqrt(5),w=sqrt(5)]) -- c**2-4*k*m = -16
+trigs %
+rule1 := rule sin(-x) == - sin(x)
+rule2 := rule cos(-x) ==   cos(x)
+rule2 rule1 %% (-3)
+draw(%,x=0..15,title=="Underdamped")
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}