Question

t?, t<3 . Express the function f(t) = le4t, 3St<5 In terms of unit step functions and compute it's Laplace transform

Answer 1

1 Que 9 - Expres the funcion fetad tt<3 3 st<5 In toms of mit step functions and compute It's haplace transform Solution We have 2. t t<3 feels 4+ 3<t<5 frta t[ult-o) - 414-8)]+&++[ult-3)-414-5)] to. ult-5) => falet [1 - ult-3)] + "[ult-3) - ult-5)] a fits to tlett +) 4(4-8) - et ult-5) Apply Laplace transfrom both sides, we get zl

» hd fltly = hq pay the left-t²) ult-3) -hf et ult-5)Y = f(s) = 2 S8 + 22 hod 24 +8)Litogeny -as had eelttsly S3 tel qu( et ca)-0(+*+6014 heut. 2º) -55 - e dla e-3s + te - fisa s-u es 20 s-4

afisl= 3S - هلے s 5-وفي + 3ع كلام پا-S S -