Question

10s2s24 (1 point) Consider the function F(s) s3 4s a. Find the partial fraction decomposition of F(s) 10s2 s24 s3 4s b. Find the inverse Laplace transform of F(s). f(t) L1 F(s)} help (formulas)

Answer 1

Given 10s2 24 F(s) 10s2s24 (४ + 4) s4s a. 10s2 24 10s2s24 3+4s bs+c +4) s(+4) a(s+4)(s)(bs +c) 10s2+s +24 put s 0, 4a 24a 6; On comparing the coefficient of s2 ab 10b= 4 On comparing the coefficient of s c 1 S= 10s2 24 10s2 +s+24 6 4s+1 (s2+4) S S 10ss24 4s+1 .+ (: L(aF ()+bG(e = aL'{F(6)}+b* {G()} ) 52+4) S ( 1 Sin at = COS at 2 a 2 2 +a S = 6 +4 S 4 1 = 6(1)+4 cos 2t +-sin 2t 2 1 sin 2 =6+4 cos 2f+- 10s2s24 1 6+4 cos 2 sin 2t 2 1 f() LF(s)) = 6+4cos 2t +sin 2t 2