Given below is an electrical network where v(t) = 390 cos t volts with initial conditions i (0) = O and i2(0) = 0. (a) Find the currents i (t) and i2(t) using Laplace Transform. [system of ODES] (b) How soon will the currents practically reach their steady state? v(t) Loon ll 2 H ll 4 H

8) Determine the z-transform of the difference equation shown below. Do not simplify or solve for anything further. Just determine the z-transform. Assume that: • y(−1) = 10, y(−2) = 20 n • x(n) = (-)" u(n) y(n) + 1½y(n y(n)+y(n-2) = 8 x(n)

Given the Z-transform 3z2-z X(z) z2+z-6 a) What are the 3 possible regions of convergence for this X(z)? b) What are the poles and zeros of X(z)? Sketch the pole-zero plot c) Assuming causal ROC in part a), invert X(z) using the method of partial-fraction expansion