If software supports 3D capability, sketch the solution curve t → (Q(t), I(t), t) for the...

If software supports 3D capability, sketch the solution curve t → (Q(t), I(t), t) for the LRC circuit with constants and initial conditions given in the indicated exercise

Given the inductance, resistance, and capacitance of a driven LRC circuit

You are also given initial conditions. Use a numerical solver to

(i) provide separate plots of the charge on the capacitor versus time (Q vs. t) and the current in the circuit versus time (I vs. t),

(ii) provide a combined plot of both charge and the current versus time, and

(iii) provide a plot of the current versus the charge (I vs. Q) in the QI phase plane.

See Exercise for aid in setting up the system. In the exercise, choose a viewing window that highlights the important features of the solutions

Sometimes the physical situation aids in the selection of substitution variables. For example, in an LRC circuit, the current is the derivative of the charge. In the LRC circuit governed by the equation

show that the substitution I = Q′ transforms the equation into the planar system

L = 1 H, R = 0 Ω, C = 1/4 F, Q(0) = 1 C, I (0) = 2 A