Question

In MATLAB Use symbolic math to solve and plot Laplace Problem 3.17. Problem 3.17 Obtain the inverse Laplace transform of each of the following 4(s-4) x1(s) 22+16) a. 4 4s b. x2s) (s2+9) (s+5)e 25 x3(s)(s+1)(s+3) c.

Answer 1

Using MATLAB Program

clc, clear all,
syms s;
%%Problem 3.7 (a)
disp('Problem 3.7 (a)')
X1=2+((4*(s-4))/((s^2)+16))
ilaplace(X1)
%%%Problem 3.7 (b)
disp('Problem 3.7 (b)')
X2=((4/s)+((4*s)/((s^2)+9)))
ilaplace(X2)
%%%Problem 3.7 (c)
disp('Problem 3.7 (c)')
X3=((s+5)*exp(-2*s))/((s+1)*(s+3))
ilaplace(X3)

Solution

Problem 3.7 (a)

X1 =

(4*s - 16)/(s^2 + 16) + 2


ans =

4*cos(4*t) - 4*sin(4*t) + 2*dirac(t)

Problem 3.7 (b)

X2 =

(4*s)/(s^2 + 9) + 4/s


ans =

4*cos(3*t) + 4

Problem 3.7 (c)

X3 =

(exp(-2*s)*(s + 5))/((s + 1)*(s + 3))


ans =

5*heaviside(t - 2)*(exp(2 - t)/2 - exp(6 - 3*t)/2) - heaviside(t - 2)*(exp(2 - t)/2 - (3*exp(6 - 3*t))/2)

>>

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