User:Egm4313.s12.team8.tclamb/R7-1

=R7.2 - Plot wave equation solution=

Problem Statement
Plot the truncated-series:
 * $$u(x,t)\,=\,\sum\limits_{j=1}^n a_j \cos(c \omega_j t) \sin(\omega_j x)$$

with $$n=5$$, and for:
 * $$t\,=\,\alpha p_1\,=\,\alpha \frac{2\pi}{c \omega_1}\,=\,\alpha\frac{2L}{c}$$
 * $$\alpha\,=\,0.5,\,1,\,1.5,\,2$$

and:
 * $$\omega_j\,=\,j\frac{\pi}{L}$$
 * $$a_j\,=\,\begin{cases} 0 \text{ for } j=2m \text{ (even)} \\ -4 / (\pi^3 j^3) \text{ for } j = 2 m + 1 \text{ (odd)} \end{cases}$$

Solution
The plots are generated with the following Mathematica code:
 * [[Image:egm4313.s12.team8.tclamb.r7.2.src.gif]]


 * [[Image:egm4313.s12.team8.tclamb.plot1.png]]
 * [[Image:egm4313.s12.team8.tclamb.plot2.png]]
 * [[Image:egm4313.s12.team8.tclamb.plot3.png]]
 * [[Image:egm4313.s12.team8.tclamb.plot4.png]]