#### 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 $$\frac{\partial u\left ( 0,t\right ) }{\partial x}=0$$.