| """ |
| Driven String + Fixed End — auto-generated. |
| """ |
| import numpy as np |
| import matplotlib.pyplot as plt |
| import matplotlib.animation as animation |
| from matplotlib.patches import Circle, Rectangle |
|
|
| L = 4.033794607093149 |
| mu = 0.08790182986007894 |
| T = 3.3334408320134097 |
| A = 0.09564982619062612 |
| f_drive = 1.5493486192174721 |
| gamma_w = 0.5118228326278383 |
| N = 200 |
| n_per_frame_in = 16 |
| duration = 12 |
| fps = 30 |
| omega = 2 * np.pi * f_drive |
| c = np.sqrt(T / mu) |
|
|
| dx = L / N |
| x_grid = np.linspace(0.0, L, N + 1) |
| n_per_frame = n_per_frame_in |
| dt = 1.0 / (fps * n_per_frame) |
| factor = (c * dt / dx) ** 2 |
| while factor >= 1.0: |
| n_per_frame *= 2 |
| dt = 1.0 / (fps * n_per_frame) |
| factor = (c * dt / dx) ** 2 |
| damp_n = 1.0 / (1.0 + gamma_w * dt) |
| damp_p = 1.0 - gamma_w * dt |
|
|
| u_curr = np.zeros(N + 1) |
| u_prev = np.zeros(N + 1) |
| n_frames = int(duration * fps) + 1 |
| U_frames = np.zeros((n_frames, N + 1)) |
| U_frames[0] = u_curr.copy() |
|
|
| for frame in range(1, n_frames): |
| for sub in range(n_per_frame): |
| t_curr = (frame - 1) / fps + (sub + 1) * dt |
| u_next = np.empty_like(u_curr) |
| lap_int = u_curr[2:] - 2 * u_curr[1:-1] + u_curr[:-2] |
| u_next[1:-1] = damp_n * (2 * u_curr[1:-1] - damp_p * u_prev[1:-1] + factor * lap_int) |
| u_next[-1] = 0.0 |
| u_next[0] = A * np.sin(omega * t_curr) |
| u_prev, u_curr = u_curr, u_next |
| U_frames[frame] = u_curr.copy() |
|
|
| fig_w, fig_h = 12.0, 4.0 |
| fig_aspect = fig_w / fig_h |
| x_lo_d = -0.40; x_hi_d = L + 0.40 |
| y_lo_d = -4.5 * A; y_hi_d = +4.5 * A |
| dx_d, dy_d = x_hi_d - x_lo_d, y_hi_d - y_lo_d |
| if dx_d / dy_d < fig_aspect: |
| extra = (fig_aspect * dy_d - dx_d) / 2.0 |
| x_lo, x_hi = x_lo_d - extra, x_hi_d + extra |
| y_lo, y_hi = y_lo_d, y_hi_d |
| else: |
| extra = (dx_d / fig_aspect - dy_d) / 2.0 |
| x_lo, x_hi = x_lo_d, x_hi_d |
| y_lo, y_hi = y_lo_d - extra, y_hi_d + extra |
|
|
| fig = plt.figure(figsize=(fig_w, fig_h), facecolor="#1a1a2e") |
| ax = fig.add_axes([0, 0, 1, 1]); ax.set_facecolor("#16213e") |
| ax.set_xlim(x_lo, x_hi); ax.set_ylim(y_lo, y_hi) |
| ax.set_aspect("equal"); ax.axis("off") |
| ax.axhline(0.0, color="#3a4357", lw=1, ls="--", zorder=0) |
| ax.plot([0, 0], [y_lo, y_hi], color="#4a4e69", lw=1.5, ls=":", zorder=1) |
| driver_dot = Circle((0, 0), 0.04, facecolor="#e63946", edgecolor="#adb5bd", lw=1.0, zorder=5) |
| ax.add_patch(driver_dot) |
| ax.add_patch(Rectangle((L, y_lo), 0.12, y_hi - y_lo, facecolor="#4a4e69", edgecolor="#adb5bd", lw=1.5, zorder=2)) |
| ax.plot([L, L], [y_lo, y_hi], color="#adb5bd", lw=2.0, zorder=3) |
| anchor = Circle((L, 0), 0.05, facecolor="#e63946", edgecolor="#adb5bd", lw=1.0, zorder=5) |
| ax.add_patch(anchor) |
| str_line, = ax.plot([], [], color="#a8dadc", lw=2.4, zorder=4) |
|
|
| def update(f): |
| u = U_frames[f] |
| str_line.set_data(x_grid, u) |
| driver_dot.center = (0, u[0]) |
| return str_line, driver_dot, anchor |
|
|
| ani = animation.FuncAnimation(fig, update, frames=n_frames, interval=1000.0/fps, blit=False) |
| ani.save("driven_string_fixed.mp4", writer=animation.FFMpegWriter(fps=fps, bitrate=1800), dpi=120) |
| plt.close(); print("Saved driven_string_fixed.mp4") |
|
|
