Problem 4. Consider the system with transfer function Y(s) 36 U(s) s²+36 If U (s) is a step input with the magnitude of 20, find y(t) (hit: use table of Laplace transforms). =
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- Solve the following question Given: look for the inverse Laplace transformation. L^-1 [3/(s-5) + 4/(s^5) + 3/(s^2+9)]Explain in your words how the Laplace transform is applied to solve a system of linear deferential equations with constant coefficients. Please respond digitally writtenI want to solve the problem of Laplace transform.
- A. Find the Laplace transforms of the given functions. 1. f(t) = 6e^(-5t)+e^3t+5(t^3)-9 2. g(t) = 4cos(4t)–9sin(4t)+2cos(10t) 3. h(t) = e^3t+cos(6t)–e^(3t)cos(6t)1. Find the laplace transform of 2e^(3t) sin 4 t 2. Simplify i²⁹ + i²¹ + i 3. Write in the form a + bi the expression i³²¹⁷-i⁴²⁷+i¹⁸A tank originally contains 640 gal of fresh water. Then water 1 containing - lb of salt per gal is poured into the tank at a rate of 2 8 gal/min, and the mixture is allowed to leave at the same rate. After 5 minutes the salt water solution flowing into the tank suddenly switches to fresh water flowing in at a rate of 8 gal/min while the solution continues to leave the tank at the same rate. Find the Laplace transform of the amount of salt y(t) in the tank. L{y} =