The longitudinal displacement of a vibrating elastic bars shown in FIGURE 13.4.7 satisfies the wave equation (1) and the conditions \left.\frac{\partial u}{\partial x}\right|_{\dot{x}=0}=0,\left.\quad \frac{\partial u}{\partial x}\right|_{x=L}=0, t>0 u(x, 0)=x,\left.\quad \frac{\partial

u}{\partial t}\right|_{t=0}=0,0