Can you please write the Matlab code for the given problem and its solution, tha

Question

Can you please write the Matlab code for the given problem and its solution, thank you.

Goal: Investigate the charge on a capacitor in an RLC circuit with varying voltage. Tools needed: ode45, plot Description: If Q(t) -charge on a capacitor at time t in an RLC circuit (with R, L and C being the resistance, inductance and capacitance, respectively) and E(t) applied voltage, then Kirchhoff's Laws give the following 2"d order diffcrential cquation for Q(t) LQ'(t) + RQ'(t)-1, Q(t) = E(t) E(t) Questions: Assume L = 1, C= 1/5, R-4 and E(t) 10 cos wt 1. Use ode45 (and plot routines) to plot the solution of (*) with Q(0) = 0 and Q'(0) = 0 over the interval 0

Explanation / Answer

MATLAB code

sol = zeros(7,2);
w = [0,0.5,1,2,4,8,16];

for i=1:7
t = 0:80;
q_init = [0;0];
[t,q] = ode45(@ode,t,q_init);

function dqdt = ode(t,q)
q1 = 0;

q2 = 0;

dqdt_1 = 0;

dqdt_2 = 0;

dqdt = [0;0];

dqdt_1 = q2;

dqdt_2 = - 4*q1 - 5*q2 + 10*cos(w(i)*t);

dqdt = [dqdt_1; dqdt_2];

end

sol(i) = [t,y];
end

for i = 1:7

plot(sol(i));

title('w = '%d' ',w(i))

xlable('t')

ylable('q')

end

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