RLC circuits, resonance and initial value

What is the governing DE for this circuit?

What is the condition for resonance?

Please share your work with us, indicating exactly where you are stuck - sothat we may know where to begin to help you.

ApBHR7pCAAEC4rG.jpg I'm not exactly sure if I'm doing this right. We've never gone over a problem quite like this in class. Most problems give you the resistance, voltage and hertz but I feel like this problem is missing information
 
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