Question: MATLAB Part 1: Use differential equation to describe a system, solve differential equation. Exercise 1: For the circuit shown below, at the moment t=0, the

MATLAB

Part 1: Use differential equation to describe a system, solve differential equation. Exercise 1: For the circuit shown below, at the moment t=0, the switch is moving from position a to position b, find Vc R1 w Vs w R (1) Write the differential equation for RC circuit after t > 0? (2) Solve the differential equation by hand, find the mathematic expression of yo. (3) If Vs = 100V, R = 80k 2, C =0.5uF, Use MATLAB to solve the same differential equation. Write a MATLAB script to calculate the time constant, plot ve up to 700ms. Include axis label, title, legend for all figures. (4) Modify your script for Vs = 100V, R = 80k22, C = 1.2 pF, calculate the time constant, plot ve up to 700ms. (5) Modify your script for Vs = 100V, R = 50k 2, C = 1.2 uF, calculate the time constant, plot ve up to 700ms (6) Plot the results of 3.4, and 5 in one figure, discuss the effect of time constant (7) Use the condition in 3, calculate the current through resistor R, plot ir up to 700ms. (8) Use the condition in 3, calculate the power of resistor R, plot pr up to 700ms

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