Question

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).

Answer 1

f Question Given th= 4 (9) Write tet in one line wing the unit step function ost <3 +73 4+ +CD=4 (+4=1 404)= { [uce-o) -(4-3)) + 4 [ ulet 3] 3 Herefore ΟΥ (b teu = { [MCA) - Uf3)] +44(4-3) t(t) = Puct) - uct-3) + 4 (-2) how Hind Laplace transform. Abbly Leplace pantoom on (0) 1-4+6+){ = L4f461)} - L {uct-3)} + 4 | face-3)? 13 fucy)}= 1383=1483-3,13 44.9) uct-02 e as 12 400? KIUCH-3)} = { } (x+382 © 123M2 = n! et 6t+ 9} 4483 + 61343 +9L???] 6 t B Lust-3) = 3= Put these values in equation B LE+(H)2 = +4 e -35 -35 35 h 2 + 83 -38 5 -35 s