Determine the equation defining the state plane for the system of Figure P12.6. Sketch trajectories in the phase plane when the following are given.

(a) \(p=1.5 \mathrm{~m}^{-1}, \omega=5 \mathrm{rad} / \mathrm{s}\)

(b) \(p=1.0 \mathrm{~m}^{-1}, \omega=5 \mathrm{rad} / \mathrm{s}\)

(c) \(p=5.097 \mathrm{~m}^{-1}, \omega=10 \mathrm{rad} / \mathrm{s}\)

FIGURE P12.6 w Parabola y=px rotates at constant w Particle of mass m moves along parabola x= generalized coordinate