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  • Pregunta: Given the following I/O equations, obtain the response y(t) using Laplace transform methods. 0.4y + y = 0 with y(0) = -2 0.4y + y = 2u(t) with u(t) = 0.7U(t), y(0) = -2 2y + 3y = u(t) with u(t) = 4U(t), y(0) = 3 2y = 3u(t) with u(t) = 4cos 6t, y(0) = 0 y + 3y + 2y = 0.5u(t) with u(t) = 0.2U(t), y(0) = 0, y(0) = -1 y + 5y + 6y = 0.5u(t) with u(t) = 6


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    Hay 2 pasos para resolver este problema.
    Solución
    Paso 1

    Given,

    y¨+5y˙+6y=0.5u(t)

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Texto de la transcripción de la imagen:
Given the following I/O equations, obtain the response y(t) using Laplace transform methods. 0.4y + y = 0 with y(0) = -2 0.4y + y = 2u(t) with u(t) = 0.7U(t), y(0) = -2 2y + 3y = u(t) with u(t) = 4U(t), y(0) = 3 2y = 3u(t) with u(t) = 4cos 6t, y(0) = 0 y + 3y + 2y = 0.5u(t) with u(t) = 0.2U(t), y(0) = 0, y(0) = -1 y + 5y + 6y = 0.5u(t) with u(t) = 6 delta(t), y(0) = 0, y(0) = 0 y + 4y + 20y = 0 with, y(0) = 2, y(0) = -0.5 2y + 12y + 68y = 0.5u(t) with u(t) = 4U(t), y(0) = 1, y(0) = 0 20y + 80y + 260y = 0.8u(t) with u(t) = 10 delta(t), y(0) = 0.2, y(0) = 0.6