Difference between revisions of "Talk:128: dPain over dt"
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Pain = c_1 (e^k_2 + d e^t)^(-k_1) + (Girl)/k_1 | Pain = c_1 (e^k_2 + d e^t)^(-k_1) + (Girl)/k_1 | ||
| − | Hopefully, d is relatively small ("days... or weeks"), thereby diminishing the time it takes for Pain to change. Significantly, k_1 needs to be positive, otherwise the first term would grow unbounded and Pain would never decrease. Assuming k_1 is positive, a | + | Hopefully, d is relatively small ("days... or weeks"), thereby diminishing the time it takes for Pain to change. Significantly, k_1 needs to be positive, otherwise the first term would grow unbounded and Pain would never decrease. Assuming k_1 is positive, a larger k_2 results in a lower initial state. Again assuming k_1 is positive, the "Girl" term guarantees there will always be a nonzero amount of Pain since Pain approaches Girl/k_1 asymptotically, unless of course "How much she's still in my life" is zero. This probably gives rise to observation "I guess there's some kind of a cutoff after years." |
--[[User:Smartin|Smartin]] ([[User talk:Smartin|talk]]) 02:33, 1 January 2013 (UTC) | --[[User:Smartin|Smartin]] ([[User talk:Smartin|talk]]) 02:33, 1 January 2013 (UTC) | ||
Revision as of 04:14, 1 January 2013
Explanation
- Since this is my first real contribution here I'm putting everything on the talk page instead of on the article itself.
The equation describes Pain as a function of Pain, time, and several constants. This is a first-order linear differential equation with possible solution:
Pain = c_1 (e^k_2 + d e^t)^(-k_1) + (Girl)/k_1
Hopefully, d is relatively small ("days... or weeks"), thereby diminishing the time it takes for Pain to change. Significantly, k_1 needs to be positive, otherwise the first term would grow unbounded and Pain would never decrease. Assuming k_1 is positive, a larger k_2 results in a lower initial state. Again assuming k_1 is positive, the "Girl" term guarantees there will always be a nonzero amount of Pain since Pain approaches Girl/k_1 asymptotically, unless of course "How much she's still in my life" is zero. This probably gives rise to observation "I guess there's some kind of a cutoff after years."
