Difference between revisions of "Team:Warwick/Modeling"
Line 31: | Line 31: | ||
+ | |||
+ | <br>By letting | ||
+ | |||
+ | |||
+ | |||
+ | |||
+ | |||
+ | <br>We can solve this differential equation using separation of variables. | ||
+ | |||
+ | |||
+ | |||
+ | |||
+ | <br>Where χ is an unknown constant. To find χ we set A=A_0 at t=0. | ||
+ | |||
+ | |||
+ | |||
+ | |||
+ | <br>Note that 4ac-b^2 is negative, so the square root cannot be calculated. We now rearrange to cancel out imaginary parts. | ||
+ | |||
+ | |||
+ | |||
+ | <br>Therfore | ||
+ | |||
+ | |||
+ | |||
+ | |||
+ | <br>Substituting the values for a, b, and c. | ||
+ | |||
+ | |||
+ | |||
+ | |||
+ | <br>Let | ||
+ | |||
+ | |||
+ | |||
+ | |||
+ | |||
+ | <br>Then | ||
Revision as of 16:52, 16 September 2015