MATLAB EXERCISE LAPLACE TRANSFORMS

HANS STIGTER AND TON VAN BOXTEL

(1) Find the Laplace transforms of the following functions (i) by hand calcula-tion, and (ii) with the help of MATLAB’s symbolic toolbox:(a) f(t) = 2 t3

(b) f(t) = cos (5 t)(c) f(t) = t e2 t

(d) f(t) = (t + 1)(2) Solve the differential equations

(a) dx(t)dt

− x(t) = 0, x(0) = −1

(b) dx(t)dt

+ a x(t) = 0, x(0) = b,

(c) d2x(t)

dt2+ 3 dx(t)

dt+ 2x(t) = 0, x(0) = −1,

dx(t)dt

= 1(3) Calculate the initial and final value limits for

(a) F (s) = 5(3 s+1) s

(b) F (s) = 73 s3+2 s2+3 s

(c) F (s) = 2 s+5(s+2) s

(4) Apply partial fraction expansion of the following expressions (i) by hand,and (ii) by Matlab(a) F (s) = 7

3 s3+2 s2+3 s

(b) F (s) = s+33 s2+2 s+3

(c) F (s) = s3+s+1

s2+2 s+3

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