Must be done in MATLAB, thank you! Problem 1 A simple series RLC circuit is driv
ID: 1874531 • Letter: M
Question
Must be done in MATLAB, thank you!
Problem 1 A simple series RLC circuit is driven by a time-varying emf, so that the differential equation for the charge, Q. on the capacitor is dr dr Take as numerical values L = 2.5 m 11·C' = 70 1, R-1.5 , to = 1.5 mV a. Compute the circuit's resonance frequency, w b. Compute, using your spread-sheet Euler's method engine, the current in this circuit as a Do this for values of the driving frequency between wR- and wR + a, where c. Plot the current 1) forwR. Identify the transient and the steady-state parts of the function of t for times ranging from 0 to 10 times the natural period (2m/) of the circuit. R/ L d. Plot the maximum current for the steady-state of the circuit as a function of driving fre- quency. Mcasure the width of the curve's peak between values equal to 1/2 the maximum. e. Compare the above numerical calculations with the exact values as computed from closed- form solutions to the differential equation. Problem 2 A mass, m, on a vertical spring of spring constant, k. is driven by a periodic force. F = Fi cos wt. It moves in a medium that exerts a velocity-dependent resistive force to its motion: Fe-. The equation of motion is thus Take as values k = 15 N/m, m 26 g. = 0.16 N.sec/m and Fo = 0.05 N a. Compute the system's resonance frequency. b. Compute, using your spread-sheet Euler's method engine, the displacement of the mass as a function of time for various driving frequencies about the resonance frequency. the curve's peak between values equal to 1/2 the maximum. you transform the one into the other with the help of simple scaling factors? c. Plot the maximum displacement as a function of driving frequency. Measure the width of d. Compare the results of this analysis with those of the RLC circuit in the first exercise. Can Problem 3 For cach of the preceding problems, derive a time-dependent expression in the steady state for the power delivered to the system. Find an expression for the time-averaged power and show its dependence upon the phase, 6. Plot this as a function of the driving frequency. 14Explanation / Answer
solution = dsolve('square(1.5*10^-3, 50) / ((2.5*10~^(-3) * 70*10^(-6))) = D2y + 1.5/(47*10^(-3)) * Dy + 1/(47*10^(-3) * 70*10^(-6)) * y', 'y(0) = 0', 'Dy(0) = 0', 'x');
ezplot('solution');
R1 = 20e3;
C1 = 235e-9;
R2 = 2e3;
C2 = 22e-9;
num = [2*R2*C1 0];
den = [C1*R1*C2*R2*2 (2*C1*R1 + M
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