Chapter 3.4, Problem 3E

In Exercises 3-8, each linear system has complex eigenvalues. For each system,
(a) find the eigenvalues;
(b) determine if the origin is a spiral sink, a spiral source, or a center;
(c) determine the natural period and natural frequency of the oscillations,
(d) determine the direction of the oscillations in the phase plane (do the solutions goclockwise or counterclockwise around the origin?); and
(e) using HPGSystemsolver, sketch the x y -phase portrait and the $x(t)$ - and $y(t)$ graphs for the solutions with the indicated initial conditions.
3. $\frac{dY}{dt}=\left(\begin{array}{rr}\hfill 0& \hfill 2\\ \hfill -2& \hfill 0\end{array}\right)Y,$ with initial condition $Y_0=(1,0)$