please follow instructions exactly and explain all steps and variables
please follow instructions exactly and explain all steps and variables 3. (9 pts) Consider the function:...
2. Consider the function 3 I < (a) Find the Laplace transform of f by direetly using the integral definition of a Laplace transform. (b) Write f in es of step functions, and use the t-shiting theorem to find the Laplace transform of f. (c) Use MATLAB to find the Laplace transform of f
2. Given 12 f(t)= ={ Ost<3 t23 (a) Write f(t) in one line using the unit step function (Heaviside function). 5 points 10 points (b) Find L{f(t)}, either by using the definition of the Laplace transform or by finding the Laplace transform of your answer to part (a).
Find the Laplace transform of the given function. f(t) = {et, Ost<2 lo, t> 2 | F(s) =
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)...
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.)
Question 9 3 pts The Laplace transform of the piecewise continuous function J4, 0< < 3 f(t) is given by 2, t> 3 2 L{f} (2 - e-st), 8 >0. S L{f} (1 – 3e-), 8>0. 8 2 L{f} (3 - e-s), 8 >0. S L{f} = (1 – 2e-st), s > 0. None of them Question 10 3 pts yll - 4y = 16 cos 2t To find the solution of the Initial-Value Problem y(0) = 0 the y...
piny 1520 7e ECW-3: Problem 16 Previous Problem List Next (1 point) The graph of f(t) is given below a. Represent f) using a combination of Heaviside step functions. Use ht - a) for the Heaviside function shifted a units horizontally f(t) = help (formulas) . Find the Laplace transform F(8) = C{f(0)} for 8 +0. F(s) = C {f(t)} = help (formulas) Note: You can earn partial credit on this problem
please answer all 4 i really need it. its greatly appreciated Les ) be a function on 10,6). The Laplace transform of t is the function F defined by the integral F(0) - Sa-mat. Use this definition to determina the Laplace transform of the following function. -- The Laplace transform of F®-(Type an expression using s as the variable.) It is defined for >(Type an integer or a fraction.) Let (U) be a function on (0.00). The Laplace transform of...
10:53 homework7 11 Homework7: Problem 11 Previous Problem List Next (1 point) Consider the function if0<t<2 a. Use the graph of this function to write it in terms of the Heaviside function. Use h(t - a for the Heaviside function shifted a units horizontally f(t) help (formulas) b. Find the Laplace transform 0. F(s) = L U(t)) for s help (formulas) Note: You can earn partial credit on this problemm. Pr
Question 9 3 pts The Laplace transform of the piecewise continuous function 4, 0<t <3 f(t) is given by t> 3 (2, L{f} = { (1 – 3e-*), s>0. O 2 L{f} (2 - e-st), 8 >0. 2 L{f} = (3 - e-st), s >0. O None of them 1 L{f} (1 – 2e -st), s >0.