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{\bf HOMEWORK 11 --- PHZ 3113}\\\vspace {2mm} 
\vspace {3mm} (April 15, 2015) \\
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For small oscillation the equations of motion of a double pendulum
are in matrix notation
$$ \left(\matrix{2&1\cr 1&1\cr}\right)\,\left(\matrix{\ddot{\phi}\cr
   \ddot{\psi}\cr}\right) + \left(\matrix{2g/l&0\cr 0&g/l\cr}\right)\,
   \left(\matrix{\phi\cr\psi\cr}\right)\ =\ 0\ . $$
\begin{enumerate}
\item Calculate the normal modes (eigenfrequencies) of the pendulum.
\item Use the eigenfrequencies and normal coordinates to write down 
      the general solution for the two angles.
\item Express the integration constants of your solution through 
      the angular positions and velocities at time $t=0$, denoted
     by $\phi_0,\, \dot{\phi}_0,\, \psi_0,\,\dot{\psi}_0$.
\end{enumerate}
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