Question

WRITE MATLAB CODE FOR IT.

Task 02: For the circuit shown in figure 12.2, the input voltage is Vi(t)-10 cos(2t) u(t) I. Plot the steady state output voltage voss(t) for t > 0 assuming zero initial conditions. I1. Determine whether the system is stable or mot? 0.5 F 2 Ohm v(t) Vo (t) 1 Ohm Figure 12.2

Answer 1

ANs 0.5F 2 n 1A volb 1H Ca) Let selve for Vosrlti Laplace dmain 2.n S IIS Vols) ciruit Laplace domain 오 tel at Vo node,

MATLAB CODE:

Nod) eqjuatihg equaiomand equatin 5 오. 2 MI5) 35+45+4 Let selve or S) and Vosst) usihg MATLAB

clc
clear all
close all

syms t s

u(t) = heaviside(t);

Vit) = 10*cos(2*t)*u(t);

VI(s) = laplace(Vi(t),t,s);
H(s) = (s^2)/(3*s^2 + 4*s + 4); % Transfer function of the given circuit
Voss(s) = H(s)*VI(s);
Voss(t) = ilaplace(Voss(s),s,t); % Steady state output

fplot(t,Voss(t),[0,10])
xlabel('t')
title('Steady State Response')
grid on

OUTPUT:

Steady State Response 2 -2 -3 6 7 8 910 2 4
(b) MATLAB CODE:

clc
clear all
close all

syms s
H(s) = (s^2)/(3*s^2 + 4*s + 4); % Transfer function of the given circuit
Poles = poles(H(s));
fprintf('Poles of the system are:\n')
disp(Poles)

OUTPUT:

Poles of the system are: (21(1/2) *2i)/3 - 2/3

Poles are located in left half of the s-plane,so that the given system is stable