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The transfer function of a system is Use Inverse Laplace Transform to determine y(t) when r(t)...
Determine the inverse Laplace transform of the function below. 5s Se s? + 85 + 25 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. - 5s se 8-1 >(t) = 2 S' + 8s + 25 (Use parentheses to clearly denote the argument of each function.)
Problem 1: Find the Laplace transform X(s) of x(0)-6cos(Sr-3)u(t-3). 10 Problem 2: (a) Find the inverse Laplace transform h() of H(s)-10s+34 (Hint: use the Laplace transform pair for Decaying Sine or Generic Oscillatory Decay.) (b) Draw the corresponding direct form II block diagram of the system described by H(s) and (c) determine the corresponding differential equation. Problem 3: Using the unilateral Laplace transform, solve the following differential equation with the given initial condition: y)+5y(0) 2u), y(0)1 Problem 4: For the...
Determine the inverse Laplace transform of the function below. Se -45 s2 + 10s + 50 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. 4s Se 2-1 s2 (t) = + 10s + 50 (Use parentheses to clearly denote the argument of each function.)
Determine the inverse Laplace transform of the function below. - 3s Se 2 S + 10s + 50 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. - 3s 3 se 2 + 10s + 50 (Use parentheses to clearly denote the argument of each function.)
Determine the inverse Laplace transform of the function below. s2 +10s +41 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Se L-1. 70 - 45 (t)= +10s +41. (Use parentheses to clearly denote the argument of each function.) 2
Determine the inverse Laplace transform of the function below. Se - 2s S2 + 8s +32 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. - 2s Se - 1 >(t) = $2 +85 +32 (Use parentheses to clearly denote the argument of each function.)
signal and system 8) By using Laplace transform determine the transfer function and the impulse response of the system with equation below. y) is the output and u) is the input to the system + 6 dt2 8) By using Laplace transform determine the transfer function and the impulse response of the system with equation below. y) is the output and u) is the input to the system + 6 dt2
Q20. (a) Describe the differential equation (3) d'y(r)_ydytr) dx dx [6 marks] (b) Apply the Laplace transform to equation (3) below and express the Y(s)-L{y(x)) in s-domain when μ4-YQ . function [14 marks] (c) Apply partial fraction decomposition upon the following system so that the denominator becomes of second order. G, (s) s4-81 [12 marks] (d) Consider the following transfer function. G,(s) (i) Find the function in time domain by applying the inverse Laplace transform on equation (5); assume zero...
Determine the system response y(t) for h(t)=u(t)+u(t-2) and x(t)=u(t). [Hint: use Laplace Transform multiplication: L[x(t)h(t)) = x(s)H(s). Useful Formula: Fourier Transform: F[f(t)] = F(w) sof(t)e-jw dt Inverse Fourier Transform: F-1[F(w)] = f (t) = 24., F(w)ejwidw Time Transformation property of Fourier Transform: f(at – to). FC)e=itoch Laplace Transform: L[f(t)] = F(s) = $© f(t)e-st dt Shifting property: L[f(t – to)u(t – to)] = e-toSF(s) e [tuce) = 1 and c [u(e) = )
Determine the inverse Laplace transform of the function below. Se - 38 88 +25 Click here to view the table of Laplace transforms Click here to view the table of properties of Laplace transforms. +8s + 25 (Use parentheses to clearly denote the argument of each function.)