Question

i want to know how to get this answer. thx

The graph of f(t) is given below. 5 4 3 y 2 1 0 2 6 8 10 = Find the Laplace transform F(5) {f(t)} by first expressing f(t) in terms of the Heaviside function. (21) +80*8+420 +4 Correct Answer: (8-25-2545) – (20-805)) Your Mark: 0/2

Answer 1

Solution:

Concept used: Equation of the line between two points (xz, yi) and (x2, y2) is given by YY_Y2 - x- X2 - Y2 - 91(x - x) + y2 X-X,

Here from the given graph

f(t) 0 2t - 4 4 0<t<2 2<t<4 4<t<8 8<t<10 0

Thus the function f(t) can be written in terms of heaviside function is given by

f(t) = 0[h(t)-h(t-2)] +(2t - 4)[h(t-2)-h(t - 4)] +4[h(t-4)-h(t-8)] + 0[h(t-8) - h(t-10)]

f(t) = (2t - 4)h(t-2) - (2t - 8)h(t - 4) – 4h(t-8)

f(t) = 2(t-2)h(t-2) – 2(t-4)h(t - 4) – 4h(t-8)... (1)

Concept used

n! L(t") = Tuus

CS e L(h(t-c) S

L(h(t -c))f(t - c) = e--sF(s)

From equation 1

L{f(t)} = F(S) = L{2(t-2)h(t-2) – 2(t-4)h(t - 4) – 4h(t-8)}

2L{(t - 2)x(t- 2)}- 2L{(t - 4)(t- 4)}- 4L{}(t - 8)}

2 2 = -23 -4s e 4 -8s -e S s 52 S

-8s f(3) = [(e-2-e -e-4-) - 2e-8

Thank you