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\begin{slide}
\centerline{\bf 2 Masses 3 Springs}

To describe the system we use a system of two second order differential equations.

\[
  m_1 \frac{d^2}{dt^2} p + c_1 \frac{d}{dt} p + k_1 (p - l_1) + k_2 (l_2 + p + q - d) = 0
 \]
 \[
  m_2 \frac{d^2}{dt^2} q + c_2 \frac{d}{dt} q + k_3 (q - l_3) + k_2 (l_2 + p + q - d) = 0
 \]
 \[
   p(0) = p_0 \qquad \frac{d}{dt}(p)(0) = p_1
\]
\[
  q(0)=q_0 \qquad \frac{d}{dt}(q)(0) = q_1 
\]
 
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\end{slide}

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\begin{slide}
Two masses attached with three springs to two stationary walls
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\begin{slide}
\centerline{\bf What happens when you get the math wrong}

\bigskip
\bigskip
Oops I made a mistake...


The explosion of the Ariane 5 rocket just after lift-off on its maiden voyage off French Guiana, on June 4, 1996, was ultimately the consequence of a simple overflow. 

{\includegraphics*[viewport = -0.5in 0in 4.5in 2in]{ariane.pdf}}

\end{slide}

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