Αποτελέσματα Αναζήτησης
PRACTICE PROBLEMS CHAPTER 6 AND 7 I. Laplace Transform 1. Find the Laplace transform of the following functions. (a) f t =sin 2t cos 2t (b) f t =cos2 3t (c) f t =te2tsin 3t (d) f t = t 3 u7 t (e) f t =t2u 3 t (f) f t ={1, if 0≤t 2, t2−4t 4, if t≥2 (g) f t ={t, if 0≤t 3,
What are the steps of solving an ODE by the Laplace transform? In what cases of solving ODEs is the present method preferable to that in Chap. 2? What property of the Laplace transform is crucial in solving ODEs? = Explain.
Laplace Transform Practice Problems (Answers on the last page) (A) Continuous Examples (no step functions): Compute the Laplace transform of the given function.
Use Properties and Basic Transforms. Find Laplace Transform. sin(5 t + 2) t. 2 et. e −. sin2 t. t sin t.
Chapter 6 Review Questions and Problems 251 1. State the Laplace transforms of a few simple functions from memory. 2. What are the steps of solving an ODE by the Laplace transform? 3. In what cases of solving ODEs is the present method preferable to that in Chap. 2? 4. What property of the Laplace transform is crucial in solving ODEs? 5. Is ...
Let Y(s) = L[y(t)] be the Laplace transform of the solution. Applying Lto the equation, we obtain the transformed equation L[0] = L[y0] L [y] = sY y(0) Y: Since L[0] = 0; we get 0 = (s 1)Y y(0); which is trivial to solve! The transformed solution to the ODE is then Y(s) = y(0) s 1:
The Laplace transform of the derivative of a function is the Laplace transform of that function multiplied by 𝑠𝑠minus the initial value of that function. ℒ𝑔𝑔̇𝑡𝑡= 𝑠𝑠𝐺𝐺𝑠𝑠−𝑔𝑔(0) (3)
