#### 2.2.1 Left end free, initial velocity zero

(10) This is animation of solution of \(\frac{\partial ^{2}u}{\partial t^{2}}=c^{2}\frac{\partial ^{2}u}{\partial x^{2}}\) for \(x\geq 0,t\geq 0\) with initial conditions \(u\left ( x,0\right ) =\left \{ \begin{array} [c]{cc}1 & 4\leq x\leq 5\\ 0 & \text{otherwise}\end{array} \right . \) and \(\frac{\partial u\left ( x,0\right ) }{\partial t}=0\) and boundary condition
\(\frac{\partial u\left ( 0,t\right ) }{\partial x}=0\).