數學題 識 La place trans form 的請進

Starting from line 7:

I[R + sL + 1/(Cs)] = E/s

I(CRs + CLs2 + 1)/(Cs) = E/s

I(CLs2 + CRs + 1) = CE

Sub all those given values, we have:

I(0.0001s2 + 0.016s + 1) = 0.002

I(s2 + 160s + 10000) = 20

I[(s + 80)2 + 3600] = 20

I[(s + 80)2 + 602] = 20

I = 20/[(s + 80)2 + 602]

= (1/3) {60/[(s + 80)2 + 602]}

Taking inverse Laplace transform:

i(t) = (1/3) e-80t sin 60t

Line 7 should be I(R + sL + 1/Cs) = E/s if L(di/dt) really = sI.