250 Ω w i250 500 Ω Σ 1500 V₁(t) 1µF = 0.5 H V2(t) +

Here is a circuit with v1(t) = sin(2000t) and v2(t) = sin(1000t). The current through the 250 ohm resistor (i250) and the 500 ohm resistor (i500) need to be found. There is no initial energy stored in the circuit and the source turns on at time t = 0.

(a) Find the state equation for this circuit.
(b) Find the output equation.
(c) Using your state and output equations, use MATLAB to plot the resistor currents for 0 <= t <= 4 ms. Use a sufficient number of samples so that the plot appears smooth.