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1- Find the Laplace transform of the following functions Of(t) = (* – 3)² (b) f(t) = sin*4t (c)f(t) = e"sinh5t

1- Find the Laplace transform of the following functions Of(t) = (* – 3)² (b) f(t) = sin*4t (c)f(t) = e"sinh5t

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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Sheet two 1- Find the Laplace transform of the following functions (a)f(t) = (t – 3)2 (b) f(t) = sin²4t (c)f(t) = e"sinh5t 2- Find inverse Laplace for the following functions 50 (b) F(s) = 5s +1 4s + 32 (a)F(s) = (c)F(s) = s3 s2 – 25 s2 – 16 3- Solve the following differential equations by Laplace transform (a) x/ + 2x = 0 ,x(0) = 1.5 (b) x –x -6x = 0 ,x(0) = 11, x(0) = 28 (c) x +9x 10e ,x(0) = 0, x(0) = 0 %3D 4- solve the following differential equations (a) x + 3x + 2x (10st< 10 1o t2 10 g(t) ,x(0) = 0,x(0) = 0 (b) x + x = g(t) = { (1 0st< 2n t 2 2n ,x(0) = 0, x(0)/ = 0 %3D (c) x// +x = 8(t - 3) ,x(0) = 0, x(0)/ = 0 5- Find (a)8(g(t))if g(t)has period 3 g(t) (1 0st<2 lo 2st<3 (b) 1 * |sinat (c) = e' * et
Transcribed Image Text:Sheet two 1- Find the Laplace transform of the following functions (a)f(t) = (t – 3)2 (b) f(t) = sin²4t (c)f(t) = e"sinh5t 2- Find inverse Laplace for the following functions 50 (b) F(s) = 5s +1 4s + 32 (a)F(s) = (c)F(s) = s3 s2 – 25 s2 – 16 3- Solve the following differential equations by Laplace transform (a) x/ + 2x = 0 ,x(0) = 1.5 (b) x –x -6x = 0 ,x(0) = 11, x(0) = 28 (c) x +9x 10e ,x(0) = 0, x(0) = 0 %3D 4- solve the following differential equations (a) x + 3x + 2x (10st< 10 1o t2 10 g(t) ,x(0) = 0,x(0) = 0 (b) x + x = g(t) = { (1 0st< 2n t 2 2n ,x(0) = 0, x(0)/ = 0 %3D (c) x// +x = 8(t - 3) ,x(0) = 0, x(0)/ = 0 5- Find (a)8(g(t))if g(t)has period 3 g(t) (1 0st<2 lo 2st<3 (b) 1 * |sinat (c) = e' * et
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