
1-3-6
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1-3-6 please with clear font thank you for your effort fe-(+1) 3 A Fond Leplace transform...
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(1 point) Use the Laplace transform to solve the following initial value problem: y6y9y 0,with y(0) 1, y (0) = -4 First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)} find the equation you get by taking the Laplace transform of the differential equation =0 Now solve for Y(s) = and write the above answer in its partial fraction decomposition, A Y(s) (s+a} s+a Y(s) Now by inverting the transform,...
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Question 3 Given the translational system shown in Figure 2, an input force, f(t) is applied to the mass, M, causing the dashpot which has a viscosity B and the spring, a stiffness coefficient of k, to compress with output displacement X(t). Input force, f(t) M O F Fixed point Displacement, X(t) Figure 2: A translational system (a) Derive the system's equation in terms of...
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(1 point) Use the Laplace transform to solve the following initial value problem: y" – 2y + 10y = 0 y(O) = 0, y' (O) = 3 First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation = 0 Now solve for Y(s) = By completing the...
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Find the Laplace transform Y (8) = L {y} of the solution of the given initial value problem. y" + 16 = S 1,0<t< , y(0) = 3, y' (0) = 2 0, <t<oo Enclose numerators and denominators in parentheses. For example, (a - b)/(1+n). Y (8) = c[1]*cos(4*t)+c[2]* sin(4*t)+1 Qe
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b and c.
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Please consider the cireuit shown below R. fl) C-4 a. Please fmd the transfer function from the input fe) to the output (). Please leave your answer in terms of R. (10 points) t y(t). Please leave b. Please design R so that impulse response has the form h(t) -Ae-* +Be-qt, i.e. it contains a decaying exponential term proportional to e-3. Also, please...
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Find the Laplace transform, F(s) of the function f(t) = t. t > 0 F(s) = ,s > 0 Question Help: Video Message instructor Submit Question Find the inverse Laplace transform of F 88 – 13 $2 – 55 – 6 3 s +1 S - 6 f(t) = Question Help: Message instructor Submit Question
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• Find the inverse Laplace Transform of the following functions: • (a) 52 +2 • (b) 3-2 +2 • (0) • (d) 5++38+2 e) (6-2)2 +4 • 32+68+11 • e) - 8+2
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'O EXPONENTIAL AND LOGARITHMIC FUNCTIONS Graphing an exponential function and its asymptote: f(x)=bº* or f(x... Graph the exponential function f (x)=2*, To graph the function, plot the points on the graph with X-values -2, -1,0, 1, and 2 Next draw the asymptote(s), and then click on the graph button. x 5 ? -12 -10 -8 -6 -4 10 12
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7. (7 pts) Consider the initial value problem y" +4y' +8y=80), (0=6, yO=0, ſo if 0 <i<6 where g(t) = 8e-21-6) if6 <i<e. (1) Take the Laplace transform of both sides of the given differential equation to create the corresponding alge- braic 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)...