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both O Apply Laplace transform on sides of the following differential equation: - eo (t) +...
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...
Apply the Laplace transform to the differential equation, and solve for Y(s). DO NOT solve the differential equation. Recall: h(t - a) is the unit step function shifted to the right a units. y" + 25y = (3t - 6)h(t – 2) - (3t – 12)h(t – 4), y(0) = y' (O) = 0 Y(8) -
Apply the Laplace transform to the differential equation, and solve for Y(s). DO NOT solve the differential equation. Recall: h(t - a) is the unit step function shifted to the right a units. y" + 25y = (4t – 8)h(t – 2) - (4t – 12)h(t – 3), y(0) = y' (O) = 0 Y(S) =
(1 point) Consider the initial value problem a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of v(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below). help (formulas) (sh2+4)Y(s)-(8s+5) Solve your equation for Y(s) b. c. Take the inverse Laplace transform of both sides of the previous equation to solve for...
Laplace transfer functions and ODE? 1) Here is a differential equation. Please find the Laplace transfer function C(s)/R(s). Note that Initial conditions are zero. ***answer provided, please show work ANS: 2) Here is a Laplace transfer function. Please find the corresponding ODE. ANS: dct) 9, ... - 4 20rc and²c(t) , - dt2 CE) 2 dct) dr(t) . - + 20r(t) + 5 - 2- d+3 dt dt² 57년 5월 S P(s) = C(9) = 52+4 R(S) (s*+1) dic tur...
Consider the initial value problem y′+3y=10e^(7t) y(0)=4. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below). b. Solve your equation for Y(s). Y(s)=L[y(t)]= c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t)....
differential equations Definition 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the integral 00 L{f(t)} = -192 e-stf(t) dt is said to be the Laplace transform of f, provided that the integral converges. 16, f(t) = {6, ost<4 t24 Complete the integral(s) that defines L{f(t)}. L{f(t)} = Datet (" dt Find L{f(t)}. (Write your answer as a function of s.) L{f(t)} = (s > 0)
9. Take the Laplace transform of both sides of the equation below and then solve for Y(s) = L{y}. Do NOT try to find y(t)! y" – 5y' – 36y = sin(3t), y(0) = 5, y'0) = 7
Let f(t) be a function on [O...). The Laplace transform of f is the function F defined by the integral F(s) = e-stf(t)dt. Use this definition to determine the Laplace transform of the following function. e3 Ost<2 f(t) = 4, 2<t for all positive si and F(s) = 2+ The Laplace transform of f(t) is F(s) = (Type exact answers.) 2+ c - 6 otherwise.
3. (30 points). Determine function y(t) from the following differential equation using the Laplace transform d?y dt2 dy. +42 + 3y = 3 dt y(0) = 2, y'(O) = 0