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Solve \(x''-x=(t^2-1)u(t-1)\) for initial conditions \(x(0)=1,x'(0)=2\) using the Laplace transform. Answer \(x(t)=(2e^{t-1}-t^{2}-1)u(t-1)-\frac{1}{2}e^{-t}+\frac{3}{2}e^{t}\)
ANSWERS TO PRACTICE PROBLEMS CHAPTER 6 AND 7 I. Laplace Transform 1. (a) Using the double angle trigonometric identity, the function f t can be rewritten as f t = 1 2 sin 4t . Thus L{f t }= 2 s2 16 (b) Using the half angle trigonometric identity, the function f t can be rewritten as f t = 1 2 1 cos 6t . Thus L{f t }= 1
Laplace Transform Practice Problems (Answers on the last page) (A) Continuous Examples (no step functions): Compute the Laplace transform of the given function.
Laplace Transforms – Practice Problems. Compute Transforms Directly. t. b. e−. 5t. c. sin at. d. sinh3t. 2. Use Properties and Basic Transforms.
6 Ιουν 2018 · Laplace Transforms – In this section we introduce the way we usually compute Laplace transforms that avoids needing to use the definition. We discuss the table of Laplace transforms used in this material and work a variety of examples illustrating the use of the table of Laplace transforms.
1. Use the rules and formulas to nd the Laplace transform of e t(t2 + 1): 2. Let f(t) = e t cos(3t): (a) From the rules and tables, what is F(s) = L[f(t)]? (b) Compute the derivative f0(t) and its Laplace transform. Verify the t-derivative rule in this case. 3. Use the Laplace transform to nd the unit impulse response and the unit step response
Practice Laplace transform, Spring 2018. On the final exam you will be given a copy of the Laplace table posted with these problems. Problem 1. Do each of the following directly from the definition of Laplace transform as an integral. (a) Compute the Laplace transform of. 1. ) = e. (b) Compute the Laplace transform of. 2. (c) Let. Prove the.
