Q 3. The total mass of a variable density rod is given by
m=
where m = mass, ?x= density,Ac(x) = cross-sectional area, x= distance along the rod, and
L = the total length of the rod. The following datahave been measured for a 20m length rod.
Determine the mass in grams to the best possible accuracy.
x,m | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 |
?, g/cm2 | 4.00 | 3.98 | 3.95 | 3.89 | 3.80 | 3.74 | 3.6 | 3.55 | 3.41 | 3.37 | 3.30 |
Ac, cm2 | 100 | 102 | 103 | 106 | 110 | 114 | 120 | 130 | 133 | 1142 | 150 |
| | | | | | | | | | | | |
Q 4.With the aid of fourth order Runge-Kutta method, solve thecompeting species model
de?ned by
where the populations and are measured in thousands andt in years. Use a step size of
0.2 for 0 ? t ? 2 and plot the trajectories ofthe populations with Matlab or GNU Octave.
