Don't you just literally add the sine waves? something like:
I think thats all you have to do. As for finding something with an exact pattern that you posted I'm not sure, but I think it could also be done by expressing the amplitude of the wave as a function of t so:
...like how in a damped wave, the amplitude decreases exponentially. In this case you would need a sort of bell shaped graph. even maybe f(t) = -t^2 + peak amplitude?