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The voltage V(s) of network is given by v(s)=3s(s+2)(s2+2s+2) plot it's pole zero diagram and hence obtain v(t)
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Solution:

Given V(s)=3s(s+2)(s2+2s+2)...(1)

zeros S=0

poles s=2,S=1+j1,S=1j1

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By pole zero diagram, & eq n (1) partial fraction expansion is:

V(s)=As+2+B(s+11j)+C(s+1+1j)...(2)

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A=3(¯OP1)(P2ˉP1)(¯P3P1)=3(21180)(2(135)(2135)=3180=3

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B=3(¯PP2)(ˉP1P2)(ˉP3P2)=3(2135)(245)(290)B=32

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C=3(¯OP3)(P1P3)(¯P2P3)=3(2135)(245)(290)C=32

Hence from (2)

V(s)=3s+2+3/2(s+1j1)+3/2(s+1+j1) Taking I.L.T. V(s)=3e2t+32e(1+j)t+32e(1j)t=3e2t+32et[ejt+ejt]=3e2t+33et[ejt+ejt2]V(s)=3e2t+3etcost

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