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13 Nov 2019
Assuming zero initial conditions (x(0) = 0ì0-0), select the Laplace transform of the response X S) for the following mass-spring system x + 2x = cost The following Laplace transforms are available: +1 s2+2 3s S2+2 s+3 2s s2+2 +5 s2+1 +2
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Beverley Smith
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All of these are to be done by hand. Find Be sure to use the chart given in class. b. 4-7 cos(60)) b. 2+3 s+2 In problems 3 and 4 Step I-Take the Laplace transform of both sides. Step Il-Solve for ty) Step IIl-Take the inverse Laplace transform of £ fy) and use the fact that y = 모-'cl { y }) to find a solution of the IVP 3. Using Laplace transforms solve the initial value problem y"+2y"-3 y = 0, y ( 0)=13"(0)-2. 4. Using Laplace transforms solve the initial value problem y', + 9 y = 2e, y ( 0 )-2, y ' (0 )-3. 5. You will be able to do these by Friday: +2s+5
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Find the equation for the current versus time t in a series circuit with inductance L = 0.1 H, resistance R = 8Ohm, and voltage V = 12V. The initial current i(0) = 2 A = (0.5 - 1.5)A = (2.0 - 1.5)A = (0.5 + 1.5)A = (2.0 + 1.5)A Find the general solution of the differential equation y'' + 5y' + 6y = 0 y(x) = C1 + C2 y(x) = C1 + C2 y(x) = C1 + C2 y(x) = C1 + C2 A series electric circuit has an inductance L = 0.5H, resistance R = 1000 Ohm, capacitance C = 1.0 Times 10-6 F, and the source voltage V = 12V. Find the equation for the current versus time t. = [C1 sin(1000t) + C2 cos(1000t)] = [C1 sin(1000t) + C2 cos(1000t)] = [C1 sin(1000t) + C2 cos(1000t)] + 0.000012 = [C1 sin(1000t) + C2 cos(1000t)] + 0.000012 Using a table of Laplace transforms, find the Laplace transform of function f(t) = . 1/(s - 3)2 1/(s + 3)2 s2/s - 3 s/(s + 3)2 Find the particular solution of the differential equation y" + y' = e2 1/6e-2t 1/6e2t -1/6e-2t -1/6e2t.
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Find the equation for the current versus time t in a series circuit with inductance L = 0.1 H, resistance R = 8Ohm, and voltage V = 12V. The initial current i(0) = 2 A = (0.5 - 1.5)A = (2.0 - 1.5)A = (0.5 + 1.5)A = (2.0 + 1.5)A Find the general solution of the differential equation y'' + 5y' + 6y = 0 y(x) = C1 + C2 y(x) = C1 + C2 y(x) = C1 + C2 y(x) = C1 + C2 A series electric circuit has an inductance L = 0.5H, resistance R = 1000 Ohm, capacitance C = 1.0 Times 10-6 F, and the source voltage V = 12V. Find the equation for the current versus time t. = [C1 sin(1000t) + C2 cos(1000t)] = [C1 sin(1000t) + C2 cos(1000t)] = [C1 sin(1000t) + C2 cos(1000t)] + 0.000012 = [C1 sin(1000t) + C2 cos(1000t)] + 0.000012 Using a table of Laplace transforms, find the Laplace transform of function f(t) = . 1/(s - 3)2 1/(s + 3)2 s2/s - 3 s/(s + 3)2 Find the particular solution of the differential equation y" + y' = e2 1/6e-2t 1/6e2t -1/6e-2t -1/6e2t.
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1 pt) Use the Laplace transform to solve the following initial value problem y',-4y' + 23y = 0 y(0) = 2, y'(0) = 3 irst using Y for the Laplace transform of y(t), i eãY-E(y(t) } ind the equation you get by taking the Laplace transform of the differential equation Y-4Y =0 Now solve for Y(s)-(2s-5)/(s^24s+25) By completing the square in the denominator and inverting the transform find y(t)= e^(2t)(2cos(sqrt(190-sin(sqrt(190
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