Differential Equations question

1. An RL circuit has an emf given (in volts) by 3 sin 2𝑡, a resistance of 10 𝑜ℎ𝑚𝑠, an inductance of 0.5 ℎ𝑒𝑛𝑟𝑦,
and an initial current of 6 𝑎𝑚𝑝𝑒𝑟𝑒𝑠. Find the current in the circuit at any time 𝑡.
2. Rewrite the steady-state current of Problem (1) in the form 𝐴𝑠𝑖𝑛(2𝑡 − ∅). The angle ∅ is called the phase
angle.

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