Question

利用MATLAB求零状态响应

Answer 1

零输入的含义是
f(t)=0，直接用dsolve求解即可（其中题目第三个方程第一项有误，应为三阶导数y'''(t)）：
>> dsolve('d2y+5*dy+6*y=0','y(0)=1,dy(0)=-1')
ans =
2*exp(-2*t)-exp(-3*t)
>> dsolve('d2y+2*dy+5*y=0','y(0)=2,dy(0)=-2')
ans =
2*exp(-t)*cos(2*t)
>> dsolve('d3y+4*d2y+5*dy+2*y=0','y(0)=0,dy(0)=-1,d2y(0)=-1')
ans =
-3*exp(-2*t)+3*exp(-t)-4*exp(-t)*t

Answer 2

syms
t
s
H=1/(s^2+5*s+4);
f=(-t+1)*(heaviside(t)-heaviside(t-2))-(heaviside(t-2)-heaviside(t-3));
F=laplace(f);
Y=F*H
y=ilaplace(Y)
ezplot(y,[-2,15])%绘制单位阶跃信号在范围之-2到15之间的波形