Transcription of Transform ee de Laplace Exercices Simples
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Transform ee de Laplace Exercices Simples
Transform ee de ee de LaplaceExercices Simples1) LaplaceCalculer les Transform ees de Laplace suivantes :a)L[(t2+t e 3t)U(t)]b)L[(t+ 2)U(t) +(t+ 3)U(t 2)]c)L[(t2+t+ 1)e 2tU(t)]2) Laplace inverseCalculer les originaux suivants :a)L 1[p+ 2(p+ 3)(p+ 4)]b)L 1[3(p+ 5)2]c)L 1[p 1(p2+ 2p+ 5)]3) Equations diff erentiellesUtiliser la Transform ee de Laplace pour d eterminer la solution particuli`ere de chacune des equations diff erentielles suivantes :a)x (t) +x(t) =tU(t) tU(t 1)condition initiale :x(0) = 0b)x (t) +x (t) =U(t)conditions initiales :{x(0) = 0x (0) = 0c)x (t) + 4x(t) = 2U(t)conditions initiales :{x(0) = 0x (0) = 1d)x (t) + 5x (t) + 4x(t) =e 2tU(t)conditions initiales :{x(0) = 1x (0) = 0e)x (t) + 2x (t) + 2x(t) = 0conditions initiales :{x(0) = 1x (0) = 1 1 / 2 LATEX 2 Transform ee de ee de LaplaceExercices d entra nement1) Calculer les Transform ees de Laplace suivantes :a)L[cos(t)e tU(t)]b)L[(5t)2e 5tU(t)]c)L[(cos(2t) sin(t))e 3tU(t)]d)L[(t2+t+ 1)e 2tU(t)]2) Calculer les originaux suivants :a)L 1[3p+ 2 1p3]b)L 1[ 2(p+ 3)2]c)L 1[5(p+ 3)(p2+ 3p+ 5)]d)L 1[pp2+ 4p+ 6]e)L 1[p(p+ 1)2]f )L 1[2p+]}}}}
Transform ee de Laplace F-IRIS1-06.tex Transform ee de Laplace Exercices Simples 1) Laplace Calculer les transform ees de Laplace suivantes : a) L h t2 + t e 3t U (t) i b) L h
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