I don't use the built-in behaviors, so this is how I would do it.

One way to write the wave equation is:

D(x,t) = A sin(kx - wt + [theta])

where w = 2(pi)f

D is the displacement from the center, k is the spring constant, x is the x position on the wave, w is [2*pi*f], f is the frequency, t is the time, and theta is the phase angle.

Since we're only concerned with one spot on the wave and not the entire thing we can let theta be zero and x be pi/2 (the maximum of a sin wave). However, if you had multiple objects you wanted to randomly wave together but not in perfect sync the easiest way to accomplish this would be by playing with the phase angle.

Now, for the behavior you asked for, I think the easiest approach would be to vary the spring constant k and not the time t. All you would need to do is solve the wave equation on every frame (remember to use a proper delta-time value and calculate the current time rather than just counting frames) and move your object to whatever displacement you come up with. When you want to change how fast it's moving you can change the spring constant k value (which isn't so constant in this case....) and it'll start moving at the new speed on its own.

Another question RamPackWobble, Is it possible to not have a range of random values? ie instead of 1-5 be its random between 1, 4, 5 or is this restricted for the clamp function?