= Solution
Now $A_0=0$, so every mass is again at rest after the pulse and $z=0+O(\epsilon^2)$. Put $k=\epsilon A_1>0$. The final transverse coordinates are
$$
\begin{pmatrix}x\\y\end{pmatrix}_{\!\rm after}
=\begin{pmatrix}1&-k\\-k&1\end{pmatrix}
\begin{pmatrix}x_0\\y_0\end{pmatrix}.
$$
The unit vectors along $x=y$ and $x=-y$ are <eigenvectors> with <eigenvalues> $1-k$ and $1+k$, respectively. Consequently an initial <circle> becomes, to first order, an <ellipse> compressed along the line $x=y$ and stretched along $x=-y$. This persistent deformation is <displacement memory>.
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