Solution
= Solution
For $1/4<r<1$, the roots are a complex-conjugate pair with modulus $\sqrt r<1$. The perturbation therefore changes sign or phase while its envelope decays:
$$
\boxed{\frac14<r<1\quad\text{gives oscillatory decay}.}
$$
= Solution
For $1/4<r<1$, the roots are a complex-conjugate pair with modulus $\sqrt r<1$. The perturbation therefore changes sign or phase while its envelope decays:
$$
\boxed{\frac14<r<1\quad\text{gives oscillatory decay}.}
$$