Question
Integral:sin[4(t -= w)]y(w) dw 622This equation is defined for t 2 0_a) Use convolution and Laplace transforms to find the Laplace transform of the solution. Obtain the solution y(t) .Enter your answer as symbolic function of S, as in these examples3*(1/5+4/s^3) Problem #8(a): 3(} 3)Enter your answer as symbolic function of t, as in these examples3*(t+2*t^2) Problem #8(b): 3(t + 2t2)Just SaveSubmit Problem #8 for GradingProblem #8 Attempt #1 Attempt #2 Your Answer +16) 8(a) 8(a) 60} 8(b) 2 + 24/
integral: sin[4(t -= w)]y(w) dw 622 This equation is defined for t 2 0_ a) Use convolution and Laplace transforms to find the Laplace transform of the solution. Obtain the solution y(t) . Enter your answer as symbolic function of S, as in these examples 3*(1/5+4/s^3) Problem #8(a): 3(} 3) Enter your answer as symbolic function of t, as in these examples 3*(t+2*t^2) Problem #8(b): 3(t + 2t2) Just Save Submit Problem #8 for Grading Problem #8 Attempt #1 Attempt #2 Your Answer +16) 8(a) 8(a) 60} 8(b) 2 + 24/2 8(b) 6 + 24/2 Your Mark: 8(a) 0/2X 8(a) 0/2x 8(b) 0/2x 8(b) 0/2x Attempt #3 Attempt #4 Attempt #5 8(a) 36} 8(a) 8(b) 8(b) 3(t + 212) 8(a) 0/2X 8(a) 8(b) 0/2x 8(b) 8(a) 8(b) 8(a) 8(b)
Answers
14. Find the Laplace transform of
$f(t) :=\int_{0}^{t} e^{v} \sin (t-v) d v$.
Let's find the laplace transform of our function F f t. So we C squared the laplace transform F of AIDS. It's equal to the integral from 0 to Infinity of t square E. Experience minus S t d C. And this is what our limits. As B approaches infinity. What do I have one over is cube minus S craig t squared minus two S t minus two E. Exponent minus S T. The interval is from server to be and this is going to give us two divided by sq yes, should be greater than so.
Let's find a laplace transform of our function f f t so we c squared. Allah please transform F of AIDS. It's equal to the integral from 0 to Infinity of t square E experience minus S t d C. And this is what our limits. As B approaches infinity. What do I have one over is cube minus S grade t squared minus two S t minus two E. Exponent minus S T. The intervals from server to be. And this is going to give us two provided by sq Yes, should be greater than so.
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