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a) F(s) = 54 (544) ESEF A(5+45) + 8 (5* +45) + (8 +45) + (574) + (Estf) (34) = 5 Az A+E=0 B+f=0 4Atc=0 4B +D 70 4C 20 40=5 c=0 A=0 E= o D =5/4. B-5 F = 5/16 5²+4 Applying Iverse Laplace gives f(t) = (-5 + + + + 1 6x2 Sinzt) ult), f(H= (- + 2 t s sinat) ult) Answer is written in terms of Integretion To get that we need to differetiate flt det + 5*++$.42.69st * Sea utzu) do 24 32 I
b) a= 15 (546) A(5²55 +365-180) + B (5²+36) + (Ls +0) (5-105+25), ass A+C =0 -SA+B-10 C + D 20 36A +25L-10D 25 -180 A +36 B +25D=0 A=-( D=-116-os 180 c +36 B + 25(-1:16-005)=0 152.5(+36B -12.520 B = -4.236 C +0.3472 sc -4.2366 to 3472 -106 -l1c-0.5 =0 c = -0.0147 A= 0.0147 B=0.4094 D=-0.483 alc- 0.0147 +0.4094 -0.01478-0-483 sus (5- s t ²+36 Applying Inverse Leplace gives 9 H = 10 10147 +0-4094 -0.0147 Cosbt -0.0805 Sin Gt] ult) differelictig gires dg (H = 0.0735 st + 2.047 teist 0.4094 ist +0.0882 singt-0.483 Cos 6t. نبای altalo.073se tě I isto 10.4094 + 4 2,047) 20-0882 Sin 6to -0.483 CG 6W 7 do please give a Thumbs up if you like my explanation. Thank you have a good day.
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