My guess is that they wanted to avoid a discontinuity in the time's derivative. At t=0 and t=w, lie'(t)=0, so the clock is smoothly transitioned into and out of

My guess is that they wanted to avoid a discontinuity in the time's derivative. At t=0 and t=w, lie'(t)=0, so the clock is smoothly transitioned into and out of a faster rate.