I’m having some fun right now in Excel trying to come up with a prediction model for wide release movies. I play a game called the Hollywood Stock Exchange and I’m trying to refine my ability to predict box office results.
I was fiddling around… charting a few things here and a few things there. Calculating the delta of this and the fraction of that. When suddenly I started seeing very regular results in particular set of graphs. Amid the chatoic swirls and the mismatched overlays of my other graphs, I had come accross some kind of regular, asymptotic line.
“I’ve seen this before.” I thought. The name of it lost in some old calculus class from the past…
Well, If I had the proper baseline equation for this function I would be able to use it in my predicition model and test it against some historic box office numbers.
I’m not sure what the data in the graph means. I was in the thick of things… calculating the derrivative of derrivatives and kind of lost my way. It has something to do with the rate at which the Weeknd BO Gross per/theater dwindles over time given that you already know the first 7 days at the BO. It could be usefull! We’ll see.
The site also says of the function that it is a “sine wave in an exponential decay envelope.”
Now, between the damped-oscillator equations and a trig function, I think I’d rather deal with the latter.
So does anyone know the equation for a “sine wave in an exponential decay envelope.”? I’m sure that there must be an equation out there that would explain this line so that it’s simple enough that you would find it in a grade 12 calc class. Because to tell you the truth, I wouldn’t know where to start with those oscillator equations!
Something like, say, f(t) = [symbol]g[/symbol]*exp([symbol]a[/symbol]t)*sin([symbol]b[/symbol]t). Be aware that Excel is nowhere near sophisticated enough to pick out the most likely values for those coefficients.
You mean I can’t have a nice simple sine equation like: **f(x) = a sin(x)^n
**?
I have no idea what all the “farads”, “ohms”, “henrys”, “jacobs” and “sally’s” would mean in my BO prediction equations. A baseline sine equation that I could shift up or down and increase the amplitude or wavelength with a flick of a coefficient would make more sense to me.
Is I(t) = (V/BL) (e^-t(R/2L)) sin(t((1/LC)-(R^2/4L^2)^1/2) really the only way?? That’s could be a nightmare in Excel!
I just finished talking with wolfstu who cut through some of my confusion and suggested:
*f(x) = e^(-x)sin(x)
as a baseline equation. He further refined the equation to:
*-50e^(-0.025x)sin(0.5x)+50
We plugged it into an online graphing calculator and the result was similar to my graphs. I realize now that a “sine wave in an exponential decay envelope” is a fancy way of saying “multiply an exponential by a sine”, and wolfstu was kind enough to point that out for me.
So thanks again guys for allowing me to pick your brains. I’m off to have some fun with this equation now!
**Wolfstu **just explained to my that your suggested equation *f(t) = g*exp(at)sin(bt) is the same thing that he suggested. I see it now. I guess my brain is just stubbornly attached to the format that I first learned when writing calc equations.
