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## Homework Statement

Find i

_{o}for t≥0.

Express your answer in terms of t, where t is in milliseconds.

There is no energy stored in the circuit in (Figure 1) when the switch is closed at t = 0.

## Homework Equations

##x(t)=x_f+[B_1cos(ω_dt)+B_2sin(ω_dt)]e^{-αt}##

## The Attempt at a Solution

Let ##i_R## be the current through the resistor, ##i_c## be the current through the capacitor, and ##V_c## be the voltage across the capacitor.

At ##t=0##:

No energy is stored in the circuit, so ##V_c(t<0)=0##, ##i_o(t<0)=0##, and since they are in parallel, ##V_o(t<0) = 0##.

Once the switch is closed, all of the current initially starts flowing through the capacitor. Since ##V_c(0^+)=V_c(0)=V_c(0^-)##, all of the voltage is across the resistor and ##i_R(0^+)=\frac{25}{125}=0.2A##.

To find the equation for ##i_o##, I believe I need ##i_f=i_o(∞)##. However, since there isn't a resistor in parallel with the LC portion of the circuit, there is nothing to absorb the energy of the oscillating current and it appears the current through the inductor oscillates forever. So what do I put for ##i_f##?