ECE 2020 Fall 2022 HW10

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Ohio State University *

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2020

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Mechanical Engineering

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Oct 30, 2023

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ECE 2020 Fall 2022 HW10 1.) Find the Laplace transform of the following functions: a. ??(?) = sin (4?)?(?) b. ??(?) = ?? −2? ?(?) c. ??(?) = (? − 1)?(? − 1) d. ??(?) = (? − 1)?(?) 2.) Use partial fraction expansion and the Laplace Transform tables to find the inverse Laplace Transform for the following functions. a. 𝐹?(?) = ? ? 2 +4?+3 b. 𝐹?(?) = 2? ? 2 +2?+2 3.) In the circuit below, v i (t) = 5e -4000t cos(3000t) V R = 12 Ω, C = 83.3μF, L = 1mH. a.) Find s. b.) Find the s-domain equation for voltage across the resistor, V O (s) c.) Find v O (t) 4.) For the circuit below, the input Vi is a 10V pulse that lasts for 1 second. R = 106 Ω, C = 44.4nF, L = 1mH. Assume all initial conditions are zero. a.) Find the equation for Vi(t) b.) Find Vi(s) c.) Find the s-domain equation for voltage across the capacitor, V o (s).Find the voltage across the capacitor, v o (t)
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