Question #42640

A 2D anisotropic lattice of coupled pendulums lies in the $x$-$y$ plane. Each pendulum has length $L = 0.625 \text{ m}$ and oscillates under gravity ($g = 10 \text{ m/s}^2$). For small angular displacements $\theta(x,y,t)$, the continuum limit wave equation is: $\frac{\partial^2 \theta}{\partial t^2} = c_x^2 \frac{\partial^2 \theta}{\partial x^2} + c_y^2 \frac{\partial^2 \theta}{\partial y^2} - \omega_0^2 \theta$ where $c_x = 3 \text{ m/s}$ and $c_y = 1.5 \text{ m/s}$ are the coupling velocities, and $\omega_0$ is the natural angular frequency of an uncoupled pendulum. A continuous harmonic driving force at the origin $(0,0)$ maintains the central pendulum's oscillation at an angular frequency $\omega = 5 \text{ rad/s}$. Assuming steady-state outward wave propagation without reflections, what is the magnitude of the phase difference between the oscillations of the pendulums at point $A(6 \text{ m}, 0)$ and point $B(0, 1.5 \text{ m})$?