Solution (source code)

= Solution

At $\tau=3/4$, the reflected <pulse> dominates the overlap. The total <displacement> is zero outside $[-3/4,0]$ and consists of straight segments through
$$
\boxed{(u,y/H)=(-3/4,0),\ (-1/4,-1),\ (0,0).}
$$
This is the inverted version of the quarter-reflected profile. The entire negative <pulse> has not yet separated from the incident <pulse>.