The equation my″ + dy′ + ky = 0 represents a damped, spring-mass system. In Exercise, valu...

The equation my″ + dy′ + ky = 0 represents a damped, spring-mass system. In Exercise, values of the parameters m, d, and k have been chosen to create a specific example of a damped, spring-mass system. We are looking for the solution y with the given initial position and velocity. Let

and use this change of variables to write each springe-mass system as a planar, autonomous system. Use pplane6 to obtain a printout of the graph of y versus t.

y″ + 2y′ + 2y = 0

y(0) = 0, y′(0) = −1