Engineering Solving RLC Circuit with Step-by-Step Guide | Circuit Diagram Included

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The discussion focuses on solving an RLC circuit after a switch is opened at t = 0. Initial conditions, including the current in the inductor and voltage across the capacitor before the switch is opened, are crucial for solving the problem. Participants emphasize the importance of showing effort before seeking help, indicating that homework assistance is not provided without prior work. A mesh equation should be established for the circuit post-switch opening, leading to a second-order differential equation. The solution involves solving this equation and applying the initial conditions to find i(t) for t ≥ 0.
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1. The switch in the circuit shown in Figure has been closed for a long time
before t = 0 but opened at t = 0. Solve for i(t) for t ≥ 0.

*Hereby I attached the circuit diagram for the question above.

And this is where I got so far.
(6ohm+6ohm)=12ohm
alpha=R/2L
= 4 Neper.
But then I don't know how to solve for the rest.
 

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We don't do homework for you. You must show some effort in order to get some help.
What were the current in the inductor and the voltage at the capacitor before the opening of the key. These are the initial conditions for your circuit.
Write the mesh equation for the circuit after the opening. You will have a second order differential equation.
Solve the differential equation and substitute the initial conditions.
 

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