MBTI
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弦&棒的振动
弦振动弦的振动方程
对弦上$x\rightarrow x+\mathrm{d}x$元段进行受力分析之后利用牛顿第二定律可以推出：
\dfrac{\partial^2\eta}{\partial x^2} = \dfrac{1}{c^2}\dfrac{\partial^2\eta}{\partial t^2}其中：$\eta$是元段的垂直位移，$c^2 = \dfrac{T}{\delta}$, $\delta = \rho S$是线密度.
通解设$\delta$和$T$均为常数，我们用行波法:
\begin{cases}
\zeta = ct + x \\
\xi = ct - x.
\end{cases}弦波方程变换为：
\dfrac{\partial^2 \eta}{\partial x^2} - \dfrac{1}{c^2}\dfrac{\partial^2\eta}{\partial t^2} = \bigg( \dfrac{\partial}{\partial x} + \dfrac{1}{c} \dfrac{\partial}{\partial t} \bigg)\b ...