# Find maximum of summation of functions

1. Jan 24, 2007

### dimensionless

$$y(t) = \sum C_{n} e^{-\gamma t} sin(n \omega t)$$

y(t) is a summation of a large number of arbitrarily decaying sinusoids with arbitrary coefficients. Find the value of t at which y(t) is a maximum.

Personally, I have doubts that this can be solved with out knowing what the constants and are and what gamma is. This is not a homework problem, so I do not know for a fact that it is solvable. What I want is some equation for t. The problem is that there could be a large number of minimums and maximums. Does anyone think this is possible without using a lot of logic and elbow grease?