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1. Solve the following differential equation using Laplace method with respect to the given initial conditions: y"+ 2y' - 3y = 2t²-10cos(2t) + 3sin(4t) -et where y(0) = 2 and y'(0) = -4

1. Solve the following differential equation using Laplace method with respect to the given initial conditions: y"+ 2y' - 3y = 2t²-10cos(2t) + 3sin(4t) -et where y(0) = 2 and y'(0) = -4

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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1. Solve the following differential equation using Laplace method with respect to the given initial conditions: y" + 2y' - 3y = 2t² - 10cos(2t) + 3sin(4t) -e³t where y(0) = 2 and y'(0) = -4 2. Find the transfer function, G(s) = X3(s)/F(s), for the given translational mechanical system. 2 N-s/m 6 N/m oooo 0000 4kg X1 (1) 2 N-s/m 4 kg -x₂ (1) oooo 6 N/m 2 N-s/m || Frictionless 4 kg x3(1) f(t) 2 N/m oooo 2 N-s/m
Transcribed Image Text:1. Solve the following differential equation using Laplace method with respect to the given initial conditions: y" + 2y' - 3y = 2t² - 10cos(2t) + 3sin(4t) -e³t where y(0) = 2 and y'(0) = -4 2. Find the transfer function, G(s) = X3(s)/F(s), for the given translational mechanical system. 2 N-s/m 6 N/m oooo 0000 4kg X1 (1) 2 N-s/m 4 kg -x₂ (1) oooo 6 N/m 2 N-s/m || Frictionless 4 kg x3(1) f(t) 2 N/m oooo 2 N-s/m
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