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      <text>22.2.3.1 Systems of second order differential equations</text>
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      <text><![CDATA[<h3><span style="color: inherit; font-family: inherit;">Systems of second order differential equations</span><br></h3>

<p>The decoupling method discussed above can be readily extended to this situation which could arise, for example, in a mechanical system consisting of coupled springs.</p>
<p>A typical example of such a system with two unknowns has the form <br>
<br>\(\qquad \ddot x=ax+by\)
<br>\(\qquad \ddot y= cx+dy\)<br>
<br>or, in matrix form,<br>
<br>\(\qquad  \ddot{\underline{x}}=A \underline{x}\) where 
<br>\(\qquad \underline{x}=\left[\begin{array}{c}x\\ y\end{array}\right]\qquad A=\left[\begin{array}{cc}a&amp;b\\
c&amp;d\end{array}\right],\qquad \ddot x=\dfrac{d^2x}{dt^2},\quad \ddot y=\dfrac{d^2y}{dt^2}.\)</p>]]></text>
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