弦振动问题演示
几何画板及绘图内容加载中，请稍等……
①本范例演示了长度为L（此处L=1）的弦上波的演化过程，通过d'Alembert公式进行模拟；②涉及的核心数学概念包括偏微分方程、定积分、函数图像、几何变换等；③作图要点提炼自构造摘要，用到了对象t, D, E, F, G, f, ω, χ, ξ, μ, κ, η, ζ, γ, β, s, r, q, λ, h, g, ν, ϕ, ψ, p, f_1等GeoGebra命令；④适合高中及以上数学学习者，用于理解波动方程的数值解法及动态变化过程。
GeoGebra 命令及参数
Numeric t(0.25)D(x) = x - floor(x)E(x) = (2 * D(x / 2))F(x) = E(x + t)G(x) = E(x - t)f(x) = If[0 ≤ F(x) ≤ 1 / 4, 0, 0]ω(x) = If[1 / 4 + 1 ≤ F(x) ≤ 1 / 2 + 1, (-4 * (F(x) - 2 + 3 / 4)), 0]χ(x) = If[1 / 4 + 1 ≤ G(x) ≤ 1 / 2 + 1, (-4 * (G(x) - 2 + 3 / 4)), 0]ξ(x) = If[1 ≤ G(x) ≤ 1 + 1 / 4, 0, 0]μ(x) = If[1 / 2 ≤ F(x) ≤ 3 / 4, (4 * (3 / 4 - F(x))), 0]κ(x) = If[1 / 2 + 1 ≤ G(x) ≤ 3 / 4 + 1, (4 * (1 / 4 - 2 + G(x))), 0]η(x) = If[1 ≤ F(x) ≤ 1 + 1 / 4, 0, 0]ζ(x) = If[3 / 4 + 1 ≤ G(x) ≤ 2, 0, 0]γ(x) = If[0 ≤ G(x) ≤ 0.25, 0, 0]β(x) = If[3 / 4 + 1 ≤ F(x) ≤ 2, 0, 0]s(x) = If[3 / 4 ≤ F(x) ≤ 1, 0, 0]r(x) = If[3 / 4 ≤ G(x) ≤ 1, 0, 0]q(x) = If[1 / 2 ≤ F(x) ≤ 3 / 4, (4 * (3 / 4 - F(x))), 0]λ(x) = If[1 / 2 + 1 ≤ F(x) ≤ 3 / 4 + 1, (4 * (1 / 4 - 2 + F(x))), 0]h(x) = If[1 / 2 ≤ G(x) ≤ 3 / 4, (4 * (3 / 4 - G(x))), 0]g(x) = If[1 / 4 ≤ G(x) ≤ 1 / 2, (4 * (G(x) - 1 / 4)), 0]ν(x) = If[1 / 4 ≤ F(x) ≤ 1 / 2, (4 * (F(x) - 1 / 4)), 0]ϕ(x) = r(x) + g(x) + h(x) + χ(x) + ξ(x) + κ(x) + ζ(x) + γ(x)ψ(x) = μ(x) + ν(x) + β(x) + ω(x) + η(x) + f(x) + s(x) + λ(x)p(x) = (1 / 2 * (ϕ(x) + ψ(x)))f_1(x) = If[0 ≤ x ≤ 1, p(x)]