Express the following functions in terms of unit step functions and find the Laplace transforms. 2...
Write the function in terms of unit step functions. Find the Laplace transform of the given function. Įt, f(t) t, ost<3 10, t23
2. Spts) Express (0) in terms of the unit step function ue(t) and find its Laplace transform. f(t) = 0, 0 St<1 2, 13t<4 Ten, t24
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,...
Write the function in terms of unit step functions. Find the Laplace transform of the given function. so, f(t) = 112, Ost< 1 t21 1949 - (22+2s+2) x Need Help? Read It Talk to a Tutor
Find the Laplace transform of the function f(t). f(t) = sint if o St<$21; f(t) = 0 if t> 21 Click the icon to view a short table of Laplace transforms. F(S) =
Write the function in terms of unit step functions. Find the Laplace transform of the given function. f(t) = {3, Ost<5 1-4, t> 5 F(s) = Need Help? Read It Watch It Talk to a Tutor
t?, t<3 . Express the function f(t) = le4t, 3St<5 In terms of unit step functions and compute it's Laplace transform
2t +1 if 0 <t< 2 Consider f(t) = { | 3t if t > 2. (a) Use the table of Laplace transforms directly to find the Laplace transform of f. (b) Express f in terms of the unit step function, then use Theorem 6.3.1 to find the Laplace transform of f.
Q1 Write the following function in terms of unit step functions. Hence, find its Laplace transform 10<tsI g(t) = le-3, +1 , 1<t 2 .22 Q2 Use Laplace transform to solve the following initial value problem: yty(o)-0 and y (0)-2 A function f(x) is periodic of period 2π and is defined by Q3 Sketch the graph of f(x) from x-2t to2 and prove that 2sinh π11 f(x)- Q4 Consider the function f(x)=2x, 0<x<1 Find the a Fourier cosine series b)...
(e) Express Laplace transforms of the following functions in terms of F(8)- (f(t)) 0 0 (e) Express Laplace transforms of the following functions in terms of F(8)- (f(t)) 0 0