I am facing problems in solving this question... I put my code .. please help

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Rama a
Rama a on 7 Jun 2021
I am facing problems in solving this question .. I will put my code and please help me to correct my working
Consider the following Differential Equation
diff(y,t,2) + A*diff(y,t) + B == C + 5*cos(1500*t)
A-Solve it (write code) for t≥0 using zero initial conditions.
B- Determine the response of the LTI systems for the given input and initial conditions: y (0)= 0, dy/dt(0) =A
A=3 B=4 C=4
syms t y(t) %symbolic variable
A = 3; B = 4; C = 4;
ode = diff(y,t,2) + A*diff(y,t) + B == C + 5*cos(1500*t); %given eqn
con1 = y(0) == 0; %y(0)
Dy(t) = diff(y,t); %y'(t)
con2 = Dy(0) == 3; %y'(0)
solution = dsolve(ode,[con1 con2]) %output y(t)
digits(3); %precision
simpleSolution = simplify(vpa(solution)) %simplified representation
fplot(solution, [0 20])
hold on
fplot(Dy(t), [0 20])
hold off
xlabel("t ->");ylabel("y(t) ->");title("Output");
  1 Comment
Walter Roberson
Walter Roberson on 8 Jun 2021
You seem to have already solved the first part?
It is not clear to me which LTI system is being referred to for the second part?

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Answers (1)

Sulaymon Eshkabilov
Sulaymon Eshkabilov on 8 Jun 2021
What are the LTI system and the input signal ?
LTI system simulation can be done easily with: tf() and lsim(). Example:
A = 1; B = 2; C = 3;
TF = tf(1, [A B C]); % LTI system: A*DDy + B*Dy + C*y = u(t)
t = linspace(0, 1, 2000);
u = cos(t);
[R, time] = lsim(TF, u, t);
plot(time, R)

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