  <li>This dynamical system is a (very) close relative of one of the systems we analyzed in this chapter.  Can you guess which one is it?  What is the connection between the two?  Extra points: support your claim with a mathematical derivation.</li>

      </ol>

    </exercise>

    <exercise><h1>Pendulum with Vibrating Base</h1>

      <ol type="a">

        <li>Identify some dynamics function $\dot q = f(q)$ whose unique equilibrium point is stable and is located in $q = 1$.</li>

        <li>Consider an