Tikzpicture with sine waveforms

Question

I have tikzpicture with sine waves. What I would want is that the red bouncy wave goes along the black sine wave until it hits the red dotted line. then drops to the blue dotted line and so on. I have now used straight lines because I don't know how to draw the red line on top of the black sine wave and then stop at the red dotted line.

\documentclass[a4paper,english,12pt]{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[xscale=0.8]
%nodes
\node [below right] at (20,0) {$t$};
\node [above left] at (0,10) {$U$};
\node [above, green] at (3,8.4) {$U(t)$};
\node [above] at (3,5.66) {$u_c (t)$};
\node [above,red] at (8,4.5) {$u_{ci} (t)$};
\node [above,blue] at (8,0.5) {$u_{ce} (t)$};
%axis
\draw [<->,ultra thick] (0,10) -- (0,-10);
\draw[->,ultra thick] (0,0)--(20,0);
%dashed lines
\draw[red,dashed,thick] (0,4.5) --(18,4.5);
\draw[red,dashed,thick] (0,-4.5) --(18,-4.5);
 \draw[blue,dashed,thick] (0,0.5) --(18,0.5);
 \draw[blue,dashed,thick] (0,-0.5) --(18,-0.5);
 %helpgrid
    \draw[gray] (0,-10) grid (18,10);
    %Green sine wave
    \draw[green,thick] (0,0) sin (3,8.4) cos (6,0) sin(9,-8.4) cos(12,0) sin(15, 8.4) cos(18,0);
    %black sine wave with lower amplitude
    \draw[thick] (0,0) sin (3,5.66) cos (6,0) sin(9,-5.66) cos(12,0) sin(15, 5.66) cos(18,0);

    %red bouncing waveform
\draw[red,ultra thick] (0,0) -- (1.7,4.5);
\draw[red, ultra thick] (1.7,4.5) -- (1.7,0.5);
\draw[red,ultra thick] (1.7,0.5) sin (3.2,2) cos (6.2,-4.5);
\draw[red,ultra thick] (6.2,-4.5) -- (6.2,-0.5);
\draw[red,ultra thick] (6.2,-0.5) -- (7.7,-4.5);
\draw[red,ultra thick] (7.7,-4.5) -- (7.7,-0.5);
\draw[red, ultra thick] (7.7,-0.5) sin (9, -2) cos (12.1, 4.5);
\draw[red,ultra thick] (12.1,4.5) -- (12.1,0.5) -- (13.7,4.5) -- (13.7, 0.5);
\draw[red,ultra thick] (13.7,0.5) sin (15,2) cos (16.3,0);

\end{tikzpicture}
\end{document}

Answer 1

I think the problem here is that to draw the function it is necessary to save a value between calls of the function (I can't see any other way of doing it, maybe I'm missing something). The following does this, although the constant \K would need be set to zero if the function was to be plotted twice.

\documentclass[tikz,border=5]{standalone}

\gdef\K{0}

\pgfmathdeclarefunction{msin}{3}{%
  \pgfmathparse{sin(#1)+\K}%
  \let\a=\pgfmathresult%
  \ifdim\a pt>#2 pt\relax
     \pgfmathparse{\K-(#2-#3)}%
     \global\let\K=\pgfmathresult%
  \fi%
  \ifdim\a pt<-#2 pt\relax%
     \pgfmathparse{\K+(#2-#3)}%
     \global\let\K=\pgfmathresult%
  \fi%
  \let\pgfmathresult=\a%
}

\def\i{0.75}
\def\j{0.125}

\begin{document}
\begin{tikzpicture}[x=.125pt, line join=round, >=stealth]

\draw (-30,0) -- (570,0);
\draw (0,-1.5) -- (0,1.5);

\draw [red, dotted]  (0, \i) -- (540, \i);
\draw [red, dotted]  (0,-\i) -- (540,-\i);
\draw [blue, dotted] (0, \j) -- (540, \j);
\draw [blue, dotted] (0,-\j) -- (540,-\j);

\draw [green] (0,0) plot [domain=0:540, samples=100] 
   (\x, 1.125*sin \x);

\draw (0,0) plot [domain=0:540, samples=100] 
   (\x, sin \x);

\draw [red] (0,0) plot [domain=0:540, samples=250] 
   (\x, {msin(\x, \i, \j)});

\end{tikzpicture}
\end{document}