Quote:
Originally Posted by Argus25
Can you then cite (attach on your next post) a single equation which will give the value with time of the voltage across the capacitor Vc(t) (initial value zero if you like) for the series R,C,L resonant circuit, after a fixed step voltage V is applied across the circuit, where your equation will accept any values of R,C, & L without attempting for some combinations of R,C & L, to take the square root of a negative number and give a meaningless result and abort the process on most computers and calculators ?
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There is a general solution, but it doesn't satisfy the bold part of your request because it's not based on the premise that taking the square root of a negative number gives a 'meaningless' result.
I should take a step back. Just to be clear, I'm not saying that the three distinct versions of the general solution that are so commonly used are in any way wrong. The general solution contains terms of the form A*exp(z) where A and z are both (potentially) complex. Interpreting the 'real world' meaning of those terms requires a familiarity with complex variables which people who use them regularly have. Unfortunately I stopped using them regularly a little more than 30 years ago, so I'd need to spend some time re-familiarising myself with them before I could write down the general solution reliably. Even more unfortunately I don't have that time to spare these days.
What brought me into this discussion was the debate about whether the three representations of the answer were distinct or not. They're really not distinct other than in terms of their ease of use with respect to calculators. They're fundamentally the same thing. But if you're constrained to using a calculator that can't handle complex variables (I've never owned one that can) then I fear you can't avoid the need for something cleverer (a human) to intervene and work out which of the three representations the calculator will be able to work with.
Cheers,
GJ