#### 2.2.2 Left end ﬁxed, initial velocity zero

This is the same problem as above, but with \(u\left ( 0,t\right ) =0\)

Source code for the above two animations is

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 \(u\left ( x,0\right ) =\left \{ \begin{array} [c]{cc}0 & 0<x<3\\ x-3 & 3<x<5\\ 7-x & 5<x<7\\ 0 & \text{otherwise}\end{array} \right . \) and \(\frac{\partial u\left ( x,0\right ) }{\partial t}=0\) and boundary condition
\(\frac{\partial u\left ( 0,t\right ) }{\partial x}=0\).

Source code for the above animation is