1. For the following functions: calculate the unisided Laplace transform; determine the poles forLaplace domain function; and specify region of convergence for s1; ift 0(1) A() ()0; if t 0(2) f(t)2e+e(3) f()-[2e +e ]u)-31

For any continuous time function x(t), the unisided Laplace Transform is expressed by equation (1).…

Answered: 1. For the following functions:…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Formulate and solve the 2nd order homogeneous differential equation for node voltage v(t). Given that the constant source current, resistor, capacitor and inductor are 10A, 12ohm, 6F and 64H, respectively. Use Laplace Transform to solve the differential having an initial condition, v’(0) = 1, v(0)=0.
Problem 4. Which gives the Laplace transforms of the given time-domain function? 1.5 ln [(s^2 + 142129)/s^2] 1.5 ln [(s^2 - 142129)/s^2] -1.5 ln [(s^2 - 142129)/s^2] -1.5 ln [(s^2 + 142129)/s^2]
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Given the following ordinary differential equation describing the dynamics of a system y'''+17y''+80y'+100y=3(u''+5u'+4u) Here, y(t) is the output and u(t) is the input. Laplace table is given below. Find the transfer function G(s) [=Y(s)/U(s)] by applying Laplace transform (all initial valus are zero) Find the poles and zeros of the system. Is the system stable or unstable? Which pole(s) is/are slow and which ones is/are fast? Find Y(s) if input is unit step function. Find initial and final values of the system by applying the theorems.
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A series circuit contains a resistor and an inductor as shown in Figure below. Determine a differential equation for the current i(f) if the resistance is R, the inductance is L, and the impressed voltage is E(t). Then determine the current i(t), with R = 4 N, L = 2 h, E (t) = cos(3t) using the ordinary variation of parameters method. Later Solve the same determined ODE using the Laplace transform (determine i(t) using Laplace transform) and compare the two Methods. for initial conditions, i(0) = 0
I need help with the question below Consider a causal linear-time invariant system described by the differential equation 2y′(t) + 6y(t) = x′(t) − 4x(t)1. Using Laplace transform technique, determine the zero-input response yz (t) if y(0−) = -3. Assume x(0−) and its higher order derivative in the vicinity of t = 0 to be zero.2. Using the Laplace transform technique, determine the zero-state response if x(t) = δ(t − π)
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1. For the following functions: calculate the unisided Laplace transform; determine the poles for Laplace domain function; and specify region of convergence for s 1; ift 0 (1) A() () 0; if t 0 (2) f(t)2e+e (3) f()-[2e +e ]u) -31