Based on the Taylor series expansion for sin, I would guess that the approach to 0 is very quick at first and then slows to a snails pace, much like x^3/3!

How would one describe it mathematically though? I have heard of rates of decay, but I am not really familiar with them.

The post also asserted that the wave would transition from a sinusoidal wave to a perfect square wave with amplitude tending to 0. Again, I am not sure how to approach that for proving it.

Thanks all for any insight