= Solution
At $\tau=1$, the incident <pulse> has left the physical half-line, so only the inverted reflected <pulse> remains. Its straight segments pass through
$$
\boxed{(u,y/H)=(-1,0),\ (-1/2,-1),\ (0,0).}
$$
It subsequently travels toward decreasing $x$ at the original <wave speed> $c$, with unchanged width $L$ and peak <amplitude> magnitude $H$.
\Image[/past-exam-of-the-mathematical-methods-ii-course-of-the-university-of-oxford/2021-pulse-reflection.png]
{title=Total displacement during reflection of a symmetric triangular pulse at a fixed end}
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