Question

Part A (Based off week 7 Workshop content) Consider the RLC circuit where R = 5, C = 1, L = 4 and VS = 8. 1. Use circuit analysis laws to show that the resistor’s voltage and inductor’s voltage can be modelled as the system of ODEs: V 0 R V 0 L = 0 R L − 1 RC − R L VR VL + 0 V 0 S 2. Solve the eigenvalues and eigenvectors of the coefficient matrix in the system of ODEs. 3. Verify your answer for question (2) by using the eig function in MATLAB (make sure you comment on whether your solutions are equivalent to MATLAB’s). 4. Solve for VR(t) and VL(t) given VR(0) = 8 and VL(0) = 0. Plot your solution in MATLAB from t = 0 to t = 30. 2 Part B (Based off week 8 workshop content) In Part B, you will be analysing the RLC circuit from Part A using numerical methods. 1. Solve the problem from Part A using the ode45 function from t = 0 to t = 30. Plot your answer and compare to your analytical solution from Part A. 2. Solve the problem from Part A using the eulerSystem function on Blackboard from t = 0 to t = 30 with N = 30 steps. Plot the solution in the same figure as your ode45 solution and comment on the accuracy of the eulerSystem solution. 3. Write a for loop that applies the eulerSystem function using N = 60, 120 and 240. Plot each solution and comment on the effect increasing N is having on the solution accuracy. 4. Adapt the eulerSystem function so that it can solve a system of ODEs using modified Euler’s method. Re-solve question (2) using your new function and comment on the accuracy of the solution compared to Euler.

Answer 1