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      <text>20.4.4.2 Two masses on springs</text>
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      <text><![CDATA[<p>Consider the vibrating system shown:</p>
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<p><img src="@@PLUGINFILE@@/Fig%28extra%292.svg" alt="A figure of 3 springs in series with 2 masses in between" width="313" height="93" class="img-responsive atto_image_button_text-bottom"></p>
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<p>As you can see, the system consists of two equal masses, both \(m\), and 3 springs of the same stiffness \(k.\) The governing differential equations can be obtained by applying Newton’s second law (‘force equals mass times acceleration’): (recall that
    a single spring of stiffness \(k\) will experience a force \(−ky\) if it is displaced a distance \(y\) from its equilibrium.)</p>
<p>In our system therefore</p>
<p>\[m \dfrac{d^2y_1}{dt^2}= −ky_1 + k(y_2 − y_1)\]</p>
<p>\[m \dfrac{d^2y_2}{dt^2}= −k(y_2 − y_1) − ky_2\]</p>
<p>which is a <strong>pair</strong> of second order differential equations.</p>]]></text>
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