I tried doing it a different way by creating a sin wave with the expression below
freq = 1
amp = 80
amp*Math.sin(freq*time*2*Math.PI);

This creates and oscillating motion which will work for the individual parts of the bird. From here I thought I could simply add the slider to the freq and control it that way. This almost works but yet falls short. If I keyframe the slider so it goes from 0 to 1 it will start with low frequencies and increase to a higher frequency, however, the frequency will be higher than 1. As soon as it hits the 1 keyframe it will level out to the proper frequency.

Similarly, when dropping from a frequency of 2 to 1 it will start at 2, drop to 0 and then instantly go back up to 1.

So maybe there is another place to add the slider.