RLC Network.

The currents in the RLC network given by the schematic diagram in Figure 9.6 are governed by the following equations:

4I'₂(t) + 52q₁(t) = 10,

13I₃(t) + 52q₁(t) = 10,

I₁(t) = I₂(t) + I₃(t)

where q₁(t) is the charge on the capacitor, I₁(t) = q'₁(t), and initially q₁ (0) = 0 coulombs and I₁(0) = 0 amps. Solve for the currents I₁, I₂, and I₃

Hint: Differentiate the first two equations, eliminate I₁, and form a normal system with x₁ = I_2, x₂ = I'₂ and x₃=I₃

You are permitted to use MATLAB when calculating eigenvalues and eigenvectors so long as you submit the code you wrote.

10 volts farads 4 henries 13 ohms 10 volts farads 4 henries 13 ohms