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(10 points) This problem is related to Problem 8.3 and 8.4 in the text. Consider the...
(10 points) This problem is related to Problems 8.16-21 in the text. Consider the differential equation...
(10 points) This problem is related to Problems 8.16-21 in the text. Consider the differential equation y" (t) + 16y'(t) + 68y(t) = –20e-4t u(t), with initial conditions y(0) = -3, and y'(0) = 4. Find the Laplace transform of the solution Y(s). Write the solution as a single fraction in s Y(s) = help (formulas) Find the partial fraction decomposition of Y(s). Enter all factors as first order terms in s, that is, all terms should be of the...
(10 points) This problem is related to Problems 8.16-21 in the text. Consider the differential equation...
(10 points) This problem is related to Problems 8.16-21 in the text. Consider the differential equation y' (t) + 7y(t) = le 4u(t), with initial condition y(0) = 2, Find the Laplace transform of the solution Y(s). Write the solution as a single fraction in s Y(s) = help (formulas) , where cis a Find the partial fraction decomposition of Y(s). Enter all factors as first order terms in s, that is, all terms should be of the form constant...
10:53 homework7 11 Homework7: Problem 11 Previous Problem List Next (1 point) Consider the function if0<t<2...
10:53 homework7 11 Homework7: Problem 11 Previous Problem List Next (1 point) Consider the function if0<t<2 a. Use the graph of this function to write it in terms of the Heaviside function. Use h(t - a for the Heaviside function shifted a units horizontally f(t) help (formulas) b. Find the Laplace transform 0. F(s) = L U(t)) for s help (formulas) Note: You can earn partial credit on this problemm. Pr
piny 1520 7e ECW-3: Problem 16 Previous Problem List Next (1 point) The graph of f(t)...
piny 1520 7e ECW-3: Problem 16 Previous Problem List Next (1 point) The graph of f(t) is given below a. Represent f) using a combination of Heaviside step functions. Use ht - a) for the Heaviside function shifted a units horizontally f(t) = help (formulas) . Find the Laplace transform F(8) = C{f(0)} for 8 +0. F(s) = C {f(t)} = help (formulas) Note: You can earn partial credit on this problem
(10 points) This problem is related to Problem 9.15 in the text. Consider the periodic function...
(10 points) This problem is related to Problem 9.15 in the text.
Consider the periodic function with period 16 given by
(10 points) This problem is related to Problem 9.15 in the text Consider the periodic function with period 16 given by if 8 t<-2 if 2 t4 if 4 t<7 if 7 t8 0 -6 f(t) = 6 0 Find the first 3 coefficients of the exponential Fourier Series for f(t), i.e., F(n) for n = -2, -1,0, 1,...
Answer all the problems please. (1 point) The graph of f(t) is given below (Click on...
Answer all the problems please.
(1 point) The graph of f(t) is given below (Click on graph to enlarge) a. Represent f(t) using a combination of Heaviside step functions. Use h(t - a) for the Heaviside function shifted a units horizontally f(t) = help (formulas) b. Find the Laplace transform F(s) = L {f(t)) for s 0. F(s) = L {f(t)) = help (formulas) (1 point) Find the inverse Laplace transform of 7s F(s) = s2-15-12 f(t)-H(t-7)*(1/7% . (Use step(t-c)...
Previous Problem Problem List Next Problem (10 points) This problem is related to Problems 9.33-9.38 in the text. We have solved differential equations using the method of undetermined coefficients (...
Previous Problem Problem List Next Problem (10 points) This problem is related to Problems 9.33-9.38 in the text. We have solved differential equations using the method of undetermined coefficients (Chapter 7) and Laplace transforms (Chapter 8). We can use Fourier series to find the particular solution of an arbitrary order differential equation - as long as the driving function is periodic and can be represented by a Fourier series In the problem description and answers, all numerical angles(phases) should be...
(t) = 0 <t< dz W sint - 4) If 4 st. a. Use the graph...
(t) = 0 <t< dz W sint - 4) If 4 st. a. Use the graph of this function to write it in terms of the Heaviside function Use hit-a) for the Heavis de function shifted a units horizontaly f(t)- help (formulas) b. Find the Laplace transform F(x) = ()} FC) - 40) help (formulas) Note: You can earn partial credit on this problem
Consider the initial value problem for function y, y" – ' - 20 y=0, y(0) =...
Consider the initial value problem for function y, y" – ' - 20 y=0, y(0) = 2, 7(0) = -4. a. (4/10) Find the Laplace Transform of the solution, Y(8) = L[y(t)]. Y(8) = M b. (6/10) Find the function y solution of the initial value problem above, g(t) = M Consider the initial value problem for function y, Y" – 8y' + 25 y=0, y(0) = 5, y(0) 3. a. (4/10) Find the Laplace Transform of the solution. Y(s)...
Consider the initial value problem for function y given by, Consider the initial value problem for...
Consider the initial value problem for function y given by,
Consider the initial value problem for function y given by, (a) Find the Laplace Transform of the source function, F(s) = L[-3 F(s) = (b) Find the Laplace Transform of the solution, Y(s) Lt) Y(s) - (c) Find the solution y(t) of the initial value problem above. s(t) Recall: If needed, the step function at c is denoted as u(t - c) -1] Help Entering Answers Preview My Anawers Submit...
(10 points) This problem is related to Problems 8.16-21 in the text. Consider the differential equation y" (t) + 16y'(t) + 68y(t) = –20e-4t u(t), with initial conditions y(0) = -3, and y'(0) = 4. Find the Laplace transform of the solution Y(s). Write the solution as a single fraction in s Y(s) = help (formulas) Find the partial fraction decomposition of Y(s). Enter all factors as first order terms in s, that is, all terms should be of the...
(10 points) This problem is related to Problems 8.16-21 in the text. Consider the differential equation y' (t) + 7y(t) = le 4u(t), with initial condition y(0) = 2, Find the Laplace transform of the solution Y(s). Write the solution as a single fraction in s Y(s) = help (formulas) , where cis a Find the partial fraction decomposition of Y(s). Enter all factors as first order terms in s, that is, all terms should be of the form constant...
10:53 homework7 11 Homework7: Problem 11 Previous Problem List Next (1 point) Consider the function if0<t<2 a. Use the graph of this function to write it in terms of the Heaviside function. Use h(t - a for the Heaviside function shifted a units horizontally f(t) help (formulas) b. Find the Laplace transform 0. F(s) = L U(t)) for s help (formulas) Note: You can earn partial credit on this problemm. Pr
piny 1520 7e ECW-3: Problem 16 Previous Problem List Next (1 point) The graph of f(t) is given below a. Represent f) using a combination of Heaviside step functions. Use ht - a) for the Heaviside function shifted a units horizontally f(t) = help (formulas) . Find the Laplace transform F(8) = C{f(0)} for 8 +0. F(s) = C {f(t)} = help (formulas) Note: You can earn partial credit on this problem
(10 points) This problem is related to Problem 9.15 in the text.
Consider the periodic function with period 16 given by
(10 points) This problem is related to Problem 9.15 in the text Consider the periodic function with period 16 given by if 8 t<-2 if 2 t4 if 4 t<7 if 7 t8 0 -6 f(t) = 6 0 Find the first 3 coefficients of the exponential Fourier Series for f(t), i.e., F(n) for n = -2, -1,0, 1,...
Answer all the problems please.
(1 point) The graph of f(t) is given below (Click on graph to enlarge) a. Represent f(t) using a combination of Heaviside step functions. Use h(t - a) for the Heaviside function shifted a units horizontally f(t) = help (formulas) b. Find the Laplace transform F(s) = L {f(t)) for s 0. F(s) = L {f(t)) = help (formulas) (1 point) Find the inverse Laplace transform of 7s F(s) = s2-15-12 f(t)-H(t-7)*(1/7% . (Use step(t-c)...
Previous Problem Problem List Next Problem (10 points) This problem is related to Problems 9.33-9.38 in the text. We have solved differential equations using the method of undetermined coefficients (Chapter 7) and Laplace transforms (Chapter 8). We can use Fourier series to find the particular solution of an arbitrary order differential equation - as long as the driving function is periodic and can be represented by a Fourier series In the problem description and answers, all numerical angles(phases) should be...
(t) = 0 <t< dz W sint - 4) If 4 st. a. Use the graph of this function to write it in terms of the Heaviside function Use hit-a) for the Heavis de function shifted a units horizontaly f(t)- help (formulas) b. Find the Laplace transform F(x) = ()} FC) - 40) help (formulas) Note: You can earn partial credit on this problem
Consider the initial value problem for function y, y" – ' - 20 y=0, y(0) = 2, 7(0) = -4. a. (4/10) Find the Laplace Transform of the solution, Y(8) = L[y(t)]. Y(8) = M b. (6/10) Find the function y solution of the initial value problem above, g(t) = M Consider the initial value problem for function y, Y" – 8y' + 25 y=0, y(0) = 5, y(0) 3. a. (4/10) Find the Laplace Transform of the solution. Y(s)...
Consider the initial value problem for function y given by,
Consider the initial value problem for function y given by, (a) Find the Laplace Transform of the source function, F(s) = L[-3 F(s) = (b) Find the Laplace Transform of the solution, Y(s) Lt) Y(s) - (c) Find the solution y(t) of the initial value problem above. s(t) Recall: If needed, the step function at c is denoted as u(t - c) -1] Help Entering Answers Preview My Anawers Submit...
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