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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.Use Laplace transform method to solve the following initial value problem y′′+2y′+y =3te^−t; y(0)=4 and y′(0)=2. and show that the answer is y(t)= e^−t(4+6t+(1/2)t^3)Let f(t) = e^t if 0<=t<1 3t-7 if t >=1 Write f(t) using step function and find the laplace transform. Also, draw the graph.
- Suppose solving an equation by Laplace transform results in 9 s Y(s) = s2 + 49' Evaluate y(0).Describe in your own words the method you would use to find the Laplace transform of the first derivative, i.e., . From 2 examples.What would the inverse Laplace Transform be for the attached function if A = 1+j4 and B = 3+j7? Please use cosines to replace complex exponentials and convert any phase angles to degrees.
- 3. (LT-1) Use the Laplace transform to find the solution to the following initial value problem: y" + 7y + 10y = 12, y(0) = -1, y'(0) = 2.Use the Laplace transform to solve x₁ = 2x1 + 3x₂ + 12e¹ x2 = x1 +4x2 with initial data x₁ (0) = -8 and x₂ (0) = 2.1. Please provide correct answers, thanks (laplace transform)