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(1 point) Sketch the graph of the function k(t) = $* (obv – 4) – 5(2...
(1 point) Sketch the graph of the function K 00 0 Use the graph to express k(t) in terms of shifts of the Heaviside step function h(t). k(t) =
(1 point) Sketch the graph of the function K 00 0 Use the graph to express k(t) in terms of shifts of the Heaviside step function h(t). k(t) =
(1 point) Sketch the graph of the function K 00 0 Use the graph to express k(t) in terms of shifts of the Heaviside step function h(t). k(t) =
(1 point) Sketch the graph of the function K 00 0 Use the graph to express k(t) in terms of shifts of the Heaviside step function h(t). k(t) =
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
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).
1. Sketch a graph of the following function: f(t)-5(H(t) -2H(t-1)+ H(t-2)) 2. Use the definiton of the Laplace Transform to show that -5s 3. Find the inverse Laplace transform of the following: (a) T(s)-( (b) Y(s)=式 ) (劫 +3s 4. Solve the the following initial value problem: Sketch the function, f(), and the solution vit) on the same graph. 5. Solve the the following initial value problem: y" + 144y = δ(t); y(0) = 0, ช่ (0) =0
(t) = 0 <t< dz W sint - 4) If 4 st. a. Use the graph of this function to write it in terms of the Heaviside function Use hit-a) for the Heavis de function shifted a units horizontaly f(t)- help (formulas) b. Find the Laplace transform F(x) = ()} FC) - 40) help (formulas) Note: You can earn partial credit on this problem
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)...
PART B
PART C
PART D
(1 point) Find the Laplace transform of f(t) = 3uſt - 2) – 4uſt - 3) – 5u(t – 5) F(s) = 1 (1 point) Consider the function f(t) = 0, t < 0 -5, 0 < t < 2 2 <t<81 4, t> 8 6, 1. Write the function in terms of unit step function f(t) = (Notation: write u(t-c) for the Heaviside step function ue(t) with step at t = c. For...
2. (1 point) Determine and sketch or graph the set 2 < 12-1+ i < 4 in the complex plane.
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.)