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By LAPLACE TRANSFORM METHOD, solve step by step the IVP a" + 6x' + 8x = 2sin (2t) , x (0) = 0, x' (0) = 1.

By LAPLACE TRANSFORM METHOD, solve step by step the IVP a" + 6x' + 8x = 2sin (2t) , x (0) = 0, x' (0) = 1.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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x(1) Consider a mass-spring-dashpot system which is modelled by ma" + cz' + kx = f(t) with the initial conditions a (0) = 0, x' (0) = 1 where the imposed external force is f(t) = 2sin(2t), the mass is m = 1, the spring constant is k = 8, and the dashpot impedance is c= 6. To find the position function x(t), please solve the following equation: By LAPLACE TRANSFORM METHOD, solve step by step the IVP x" + 6x' + 8x = 2sin (2t), x (0) = 0, x' (0) = 1. (The answers including other methods will be worth "zero" points)
Transcribed Image Text:x(1) Consider a mass-spring-dashpot system which is modelled by ma" + cz' + kx = f(t) with the initial conditions a (0) = 0, x' (0) = 1 where the imposed external force is f(t) = 2sin(2t), the mass is m = 1, the spring constant is k = 8, and the dashpot impedance is c= 6. To find the position function x(t), please solve the following equation: By LAPLACE TRANSFORM METHOD, solve step by step the IVP x" + 6x' + 8x = 2sin (2t), x (0) = 0, x' (0) = 1. (The answers including other methods will be worth "zero" points)
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