27. y'' + 25y = sin(4t),
y(0) = 0, y'(0) = 0.
Plot the component curves and the orbit, the latter for the rectangle |y|< 0.25 and |y'|< 1.
28. Hearts and Eyes: Find a solution formula for y'' + 25y = sin&(wt), where w is not equal 5. Plot the solution curve of the IVP with y(0) = y'(0), where w=4. Plot the orbit for 0< t <20 in the rectangle |y| < 0.1, -0.5 < |y'| < 0.3.
Repeat with w=1. Overlay the graphs.
The solution shows how to solve the required differential equations and provides the graphs that show an interesting behavior.