Circuitos ii

14-4-1 Determine f(t) para:
Fs=s+3s3+3s²+6s+4
Solução:
Fs=s+3s+1s+1+j3(s+1-j3) → Fs=s+3s+1(s2+2s+4)
Temos:
Fs=s+3s+1s2+2s+4=As+1+Bs+Cs2+2s+4 s+3=As2+2s+4++s+1(Bs+C)
S=-1→2=A1-2+4→A=23
S+3=As2+2s+4+Bs²+Cs+Bs+C
S+3=A+Bs2+ 2A+B+Cs+4A+C
Logo:
A+B=0→B =-23
2A+B+C=1
4A+C=3→423+C=3→C=3-83→C=13
Com Isso:
Fs=23s+1+-23s+13s²+2s+4→Fs=23s+1+-23s+1+1s+12+3
Fs=23s+1+23(s+1)s+12+3+1s+12+3 ft=23e-t-23e-tcos3t+13e-tsen(3t) 14-4-2 Determine f(t) para:
Fs=s²-2s+1s3+3s²+4s+2
Solução:
Fs=s2-2s+1s+1s2+2s+1=As+1+Bs+Cs2+2s+2
s²-2s+1=As2+2s+2+s+1Bs+C s2-2s+1=As2+2s+2+Bs2+B+Cs+C s2-2s+1=A+Bs2+2A+B+Cs+2A+C
Observe que para s=-1
1+2+1=A1-2+2
A=4
Temos que:
A+B=1→B=-3
2A+B+C=-2
2A+C=1→C=-7
Logo:
Fs=4s+1+-3s-7s2+2s+2→ Fs=4s+1+-3s-1-4s+12+1
Fs=4s+1-3×4s+12+1
ft=4e-t-3e-tcost-4e-tsentu(t)

14-4-3 Determine f(t) para:
Fs=5s-1s3-3s-2
Solução:
Fs=5s-1s+1s+1(s-2)→Fs=5s-1s+12+(s-2)
5s-1s+12s-2=As+1+Bs+12+Cs-2
5s+1=As+1s-2+Bs-2+C(s+1)²
s=-1→-3B=-6→B=2 s=2→9C=9→C=1 A+C=0→A=-1
Logo:
Fs=-1s+1+2s+12+1s-2 ft=-e-t+2te-t+e2tu(t) 14-4-4 Determine a transformada inversa de:
Ys=1s3+3s²+4s+2

Solução:

Ys=1s+1s2+2s+2=As+1+Bs+Cs2+2s+2
1=As2+2s+2+s+1Bs+C
s=-1→A=1
A+B=0→B=-1
C+B+2A=0→C=-1
Logo:
Ys=1s+1-s+1s+12+1 yt=e-t-e-tcostut yt=e-t(1-cos⁡(t))u(t)

14-4-5 Determine a transformada inversa de:
Fs=2s+6s+1(s²+2s+5)

Solução:
2s+6s+1s2+2s+5=As+1+Bs+Cs2+2s+5
As2+2s+5+s+1Bs+C=2s+6 s=-1→4A=4→A=1 A+B=0→B=-1
2A+C+B=2→C=1
Logo:
Fs=1s+1+-s+1s+12+4
Fs=1s+1+-s+1+2s+12+22
Fs=1s+1-(s+1)s+12+2²+2s+12+2²
ft=e-t-e-tcos2t+e-tsen2tut

14-4-6 Determine a transformada inversa de:
Fs=2s+6ss2+3s+2

Solução:
Fs=2s+6ss+1s+2=As+Bs+1+Cs+2
2s+6=As+1s+2+Bss+2+Cs+1s s=0→A=3 s=-1→B=-4 s=-2→C=1 Fs=3s-4s+1+1s+2 ft=3-4e-t+2e-2tut 14-4-7 Prove que:
L-1=cs+(ca-ωd)s+a2+ω²
é ft=me-atcosωt+θ, onde m=c2+d2 e θ=tan-1dc.

Solução: cs+ca-ωds+a2+ω2=cs+a-ωds+a2+ω2=cs+as+a2+ω2-dωs+a2+ω2 cL-1s+as+a2+ω2-dL-1ωs+a2+ω2= ce-atcosωt-de-atsen ωt