Question

III. When solving this problem show all the steps needed to transform the expressions into ones that can be (10) found in the table and indicate the entry of the table used in each step. a) Find the Laplace transform F(s) of the function (5+234 +5e-2) cos(6t) b) Find the inverse Laplace transform f(t) of the function F(s) = 2 s2 + 2s + 5

Answer 1

Solution 3£ (a) (ste tse e2t) cos (6+) 3t - 5.COSC6+) te!cos (6+) +50 2t cos(st): Apply Laplace transform we get F(S)=l{5.cos(6+)}+ COS (G)} L&5e?€ cos (st)} 25L{cos (61)] 1 tlf cst costs-173 +5l{eet cos (6) Lşezt + 5-3 = 5:8 82 +36 + (3-3)²+36 +5. Sta (3+2)2+36

since, L{cos (at)} = 2 84792 and. Lş eatco's cbt)} . s-q (8-9) ²7.62 : Laplace transform of 1 (57e7se?!) cos (64) .- is FO) = 5.3 8-3 + g²+36 (8-3) F161 +5(3+2) (512)416

2 6) Fl) = 23375 Apply inverse Laphile transform on both side . als 2 2. l{ FC 5)]=8+23+5 =T'{ ;$25:174] Ez remon=76032] fH) = ēt sin(24) sinar, be I'{[5+a) ?7(b)? 1 i -at sincbt) '{372375] =e+sin(24) = fit)