Applied Mathematics Laplace Transforms
2. Let t if 5 < t < 10 f(t) = -{ e3t if t > 10 Use the Heaviside step function to evaluate the Laplace of f. (4 pts.) 3. Find the inverse Laplace transform of the following functions: (i) F(s) = 4s +5 s(s2 + 4s + 5) (3 pts.) -35 (ii) G(s) = 4s + 5 s(s2 + 4s + 5) е (you may use part (i)) (2 pts.)
Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your answer as a function of t.) ℒ−1 6s − 12 (s2 + s)(s2 + 1) Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your answer as a function of t.) il 65 - 12 (s2 + s) (s2 + 1)
f(t) F(S) (s > 0) S (s > 0) n! t" ( no) (s > 0) 5+1 T(a + 1) 1a (a > -1) (s > 0) $4+1 (s > 0) S-a 1. Let f(t) be a function on [0,-). Find the Laplace transform using the definition of the following functions: a. X(t) = 7t2 b. flt) 13t+18 2. Use the table to thexight to find the Laplace transform of the following function. a. f(t)=t-4e2t b. f(t) = (5 +t)2...
Answer all the problems please. (1 point) The graph of f(t) is given below (Click on graph to enlarge) a. Represent f(t) using a combination of Heaviside step functions. Use h(t - a) for the Heaviside function shifted a units horizontally f(t) = help (formulas) b. Find the Laplace transform F(s) = L {f(t)) for s 0. F(s) = L {f(t)) = help (formulas) (1 point) Find the inverse Laplace transform of 7s F(s) = s2-15-12 f(t)-H(t-7)*(1/7% . (Use step(t-c)...
Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t ≥ 0. Then the integral ℒ{f(t)} = ∞ e−stf(t) dt 0 is said to be the Laplace transform of f, provided that the integral converges. Find ℒ{f(t)}. (Write your answer as a function of s.) ℒ{f(t)} = (s > 0) Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform et f be a function defined for t2 0. Then the integral is said to be the Laplace...
Let f(t) be a function on [0,00). The Laplace transform of fis the function F defined by the integral F(s)= si e-stf(t)dt. Use this definition to determine the Laplace transform of the following function. 4 0<t<2 f(t)= 3, 2<t -8 The Laplace transform of f(t) is F(s) for all positive si and F(s)=2+ otherwise.
Let f(t) be a function on [0, 0). The Laplace transform of f is the function F defined by the integral F(s) = e-stf(t)dt. Use this definition to determine the Laplace transform of the following function. 0 est 0<t<1 f(t) = 1 <t for all positive sand F(s) = 1 + 5 -5 otherwise. The Laplace transform of f(t) is F(s) = (Type exact answers.)
Let f(t) be a function on [0, 0). The Laplace transform of f is the function defined by the integral Foto F(s) = e - st()dt. Use this definition to determine the Laplace transform of the following function. 0 e2t, 0<t<3 f(t) = 3<t for all positive si -6 and F(s) = 3+2 e otherwise. The Laplace transform of f(t) is F(s) = (Type exact answers.)
(3) Let f(t) := (sint)/t, with the understanding that f(0) = 1 (for reasons which should be obvious from your study of limits in Calculus 1). (a) Show that ļf(t) 1 forall t. (Note that f is an even function, so you can assume t0. In fact, we will only be concerned with f (t) for t 20 in this problem.) The Laplace transform F(s) of f (t) is therefore defined for all s >0 (b) Show that -1/s <...
Let f(t) be a function on [0, 0). The Laplace transform of fis the function F defined by the integral F(s) = S e-stat)at. Use this definition to determine the Laplace transform of the following function. 0 € 5 0<t<3 f(t) = 2 3<t 2 and F(s) = 3+ - 15 otherwise The Laplace transform of f(t) is F(s) = for all positive st[ (Type exact answers.)