I have the following differential equation:
[eqn] LQ'' + RQ' + \frac{Q}{C} = 230 \sqrt{2} \sin(\omega \pi) [/eqn]
I want to know if I plug this into a function correctly. I put [math]Q' = I[/math]. Then we get:
[eqn] LI' + RI + \frac{Q}{C} = 230 \sqrt{2} \sin( \omega \pi ) [/eqn]
If we then define the vector [math] \mathbf{y} [/math] as [math]y_1 = I[/math] and [math]y_2 = Q[/math]. We get:
[eqn] y_1' = \frac{230 \sqrt{2} \sin ( \omega \pi )}{L} - \frac{R y_1}{L} - \frac{ y_2 }{LC} [/eqn]
[eqn] y_2' = y_1 [/eqn]
Plugging this into a function file we would get:
cont'd in next post.