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+\def\rload{R_{\rm load}}
+\def\opt#1{\vskip0pt plus #1\vskip 0pt plus -#1}
\input ../format
\titlesub{Part 3: Executive Summary}{Mystery Circuit}
+\input ../com
+
+\section{Matrix Representation}
+
+To determine the relevant properties of the linear system, matrix form
+is useful:
+\def\x{{\bf x}}
+$$\x' =
+{1\over R_1C_1C_2\rload}\left(
+\pmatrix{0&-C_2\rload&0 \cr
+ *&* &* \cr
+ 0&C_2R_1 &-C_2\rload} \x +
+\pmatrix{\omega\cos(\omega t)\cr
+ \omega\cos(\omega t)\cr
+ 0}
+\right).
+$$
+
+{\it *Linearly dependent, meaning a trivial eigenvalue of 0}
+
+\def\bu{\par\leavevmode\llap{\hbox to \parindent{\hfil $\bullet$ \hfil}}}
+\opt{.15fil}
+\noindent The eigenvalues and respective eigenvectors are:
+
+\bu $\lambda_1 = 0, v_1 = \pmatrix{1\cr0\cr0}$
+
+\def\num{\pmatrix{0\cr C_2\rload\cr C_2R_1}}
+\bu $\lambda_2 = -C_2\rload, v_2 = \num$
+
+\bu $\lambda_3 = -C_2\rload, v_2 = \pmatrix{0\cr0\cr1}$
+
+This gives the solution to the homogenous system
+$$D_1\pmatrix{1\cr0\cr0} + D_2e^{-C_2\rload t}\num
++ D_3te^{-C_2\rload t}\pmatrix{0\cr0\cr1}.$$
+
+Extending to the nonhomogenous system,
+
\bye