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With the set up of the circuit, would it suffice just to have the dc supply with a 'gate' that stops/allows through the dc current with a frequency of 50 Hz, and then an inductor connected to this is series and a capacitor conected to the inductor in series? Would the output be ac? I don't quite understand how to complete the circuit either...

If the above is a good way to go, is there a way to show mathematically that sinusoidal current is the output? I am still trying to get my head around this, but from what I understand the capacitor will initially be charging with a large current and the current will be decreasing. It would be decreasing exponentially, but the inductor resists the change in current so that it ends up decreasing sinusoidally, and then when the dc current is off the capacitor discharges with an initial high current which decreases exponentially, but the inductor decreases this change so that it is sinusoidal?

I have spent many hours trying to find a good YouTube video or link, but with no luck! I think it has something to do with RLC as this seemed to crop up a lot, although I don't really understand these circuits...

Thank you in advance for any help! :)