3. [24 pts] For the following piecewise functions f(t), (i) sketch a plot of f(t), (ii)...
a) i. Express in terms of the unit step function, the piecewise continuous causal functions (2t2, Ost<3 F(t) = {t + 4, 3 st<5 9, t25 [3 marks] ii. Use Laplace transforms to solve the initial value problem a) 7" + 16y = 4cos3t + s(t – 1/3) where y(0) = 0 and y'(0) = 0. [7 Marks) E.K. Donkoh (Ph.D) or [7 marks) B) y' – 3y = F(t), where y(0) = 0 and (sint, Osts F(t) = 1,...
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.
Write the following function in terms of Heaviside functions and then find the Laplace transform. Write the following function in terms of Heaviside functions and then find the Laplace transform. f(t) = { ft, if 0 st 51 1, if 1 st
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.)
please follow instructions exactly and explain all steps and variables 3. (9 pts) Consider the function: (1-t, t < 4, f(t) = { 12 - 16, 24. a. Represent f(t) using a combination of Heaviside step functions, h(t -c). b. Find the Laplace transform F(s) = L{f(t)}. Do not use the integral definition of the Laplace transform.
The Laplace transform of the piecewise continuous function $4, 0<t<3 f(t) is given by 2, t> 3 1 L{f} (1 – 2e-st), 8 >0. S None of them L{f} = (1 – 3e®), s>0. 2 L{f} (3 - e-), 8 >0. S 2 L{f} (2-est), s >0. S
The Laplace transform of the piecewise continuous function $4, 0<t<3 f(t) is given by 2, t> 3 1 L{f} (1 – 2e-st), 8 >0. S None of them L{f} = (1 – 3e®), s>0. 2 L{f} (3 - e-), 8 >0. S 2 L{f} (2-est), s >0. S
(1 point) Sketch the graph of the function k(t) = $* (obv – 4) – 5(2 – 8)) dw, Ost<co Use the graph to express k(t) in terms of shifts of the Heaviside step function. Use h(t) for the Heaviside function. k(t) =
9–27. For each of the following functions f(t), (a) express f(t) in terms of on-off switches X[a,b)(t), (b) express f(t) in terms of translates h(t – c) of the Heaviside function h(t), and (c) compute the Laplace transform F(s) = £{f(t)}. so if 0 <t<2 It-2 if 2 <t<oo So if 0 <t<2 It if 2 <t< oo 11. 40) - ſo if 0 <t< 2 It +2 if 2 <t<oo 12. f(t) = {o |(t – 4)2 if0 <1<4...
Evaluate piecewise-defined functions Question Given the following piecewise function, evaluate /(-4). - 4x + 3 f(x) = x < 0 Osr<3 3S 2? + 2 Do not include "f(-4) =" in your answer. Provide your answer below: