Solution
= Solution
Now $\dot U=-|\nabla U|^2+U_y\cos\omega t$, whose second term has either sign. Near the minimum, $\xi=C e^{-6t}$ and $\dot\eta+4\eta=\cos\omega t$, so
$$
\eta=C_2e^{-4t}+\frac{4\cos\omega t+\omega\sin\omega t}{16+\omega^2}.
$$
= Solution
Now $\dot U=-|\nabla U|^2+U_y\cos\omega t$, whose second term has either sign. Near the minimum, $\xi=C e^{-6t}$ and $\dot\eta+4\eta=\cos\omega t$, so
$$
\eta=C_2e^{-4t}+\frac{4\cos\omega t+\omega\sin\omega t}{16+\omega^2}.
$$