1. Take the differential equation given in Hw 07A-Pr. 1
HW: 07B
Problem 1:
Take the differential equation given in Hw 07A-Pr. 1
q(x): Input, y(x):Output
a) Write transfer function.
b) If input is q(x)=-2.3e-0.6xcos(7x+1.2) find the output with computer.
c) Write the form for impuls output by using computer codes.
d) If the input is step input with the magnitude 5, write the output. Write steady state value.
Answer:
b) s=-0.6+7i;hs=2/(3*s^3+9.3*s^ *s );abs(hs),angle(hs)
c) h(x)=A1 e-0.4xcos(4.6x-φ)+A2e-2.3x
h(x)= e-0.4xcos(4.6x-2.75) e-2.3x
d) h(x)=A1 e-0.4xcos(4.6x-φ)+A2e-2.3x

2. Problem 2:
Take the differential equation given in Hw 07A-Pr. 1.
q(x): Input, y(x):Output
a) Eigenvalues are : s1,2 = -0.4±4.6i, s3 = Is the output stationary or not?
b) Write the program codes for partial praction expansion, if the step input with value 5. If the partial fraction terms for numerator and denominator are: numerator : i, i, , 0.068; denominator : s-( i), s-( i), s+2.3, s . Find the output.
Answer:
a) Steady-state
b) p1=5*[2];p2=[3,9.3,69.48, ,0];[r,p,k]=residue(p1,p2)
y(x)=0.0315e-0.4xcos(4.6x ) e-2.3x+0.068