LISTA DE EXERCÍCIOS - TRANSFORMADA DE LAPLACE
1) Determine as transformadas das funções:
(a) f(t) = t3+ 3cos(2t)
(b) f(t) = 5e2t+ 7e−t
(c) f(t) = 2e2tsin(t) + cos(2t)
(d) f(t) = 1 + cosh(5t)
(e) f(t) = cos2(2t) + sin(3t)
(f) f(t) = e3tcos(2t) + t3e−t
2) Determine a transformada inversa de Laplace das funções:
(a) 1
s2+4
(b) s+3
s2+2s+5
(c) s
s2−s+17/4
(d) 2s2
(s−1)(s2+1)
(e) 2s−13
s3−4s2+13s
(f) 2s−2
s2−s+1
(g) s
(s2+9)2
(h) 1
2s3−4s2+2
3) Use a transformada de Laplace para resolver o problema de valor inicial:
(a) y00 +y=sin(2t)y(0) = y0(0) = 0
(b) y00 +y=cos(3t)y(0) = 1 y0(0) = 0
(c) y00 + 3y0+ 2y=t y(0) = 0 y0(0) = 2
(d) y00 + 6y0+ 25 = 0 y(0) = 2 y0(0) = 3
(e) y00 −4y= 3t y(0) = 0 y0(0) = 0
(f) y0−y= 1 + tety(0) = 0
(g) y00 + 4y0+ 8y=e−ty(0) = y0(0) = 0
(h) y00 −y0=etcos(t)y(0) = 0 y0(0) = 0
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