Pulsing Niagara particles on a spline

Once again, Hi.

I am trying to get a synchronized pulsing movement of Niagara particles along a spline.
This is what I have done so far:

Which is this function f(x)=Asin(Bx)+(mx+c), and the particle goes fast, then slow, then fast, then slow again and so on until it dies:

The function above gives me a pulsing effect, but I would like it to be more like this red line, instead of the green:


I basically want to be able to control for how long the slow and the fast movements should be.

Any ideas how I can create that kind of effect or how the function would be?