/sci/ - Science & Math

>>12733278
>the solution looks something like cosine
You're not wrong! Since g & L are both positive, solving for x in the characteristic equation gives us [math] x = \pm \sqrt{-\frac{g}{L}} = \pm i\sqrt{\frac{g}{L}} [/math]. Thus our exponential solutions take complex arguments and are complex conjugates of each other, so we can express them in terms of sin & cos instead if we like. You could also use [math] \theta (t) = A\cos(\omega t) [/math] as your initial ansatz, but I prefer exponentials since they're more general, and I'm in EE so working with complex numbers is just more natural.

>>12688762
No problem. Diff eqs can be pretty weird and unintuitive when you start out, even more so when you're working with circuits instead of mechanical systems. Good luck with your studies!