2lee

My matrix is

matrix = [

  [0,1,3,2,4],

  [2,0,2,2,2],

  [3,1,0,1,3],

  [4,4,3,0,3],

  [2,4,4,4,0]

]

Team 5: rating = 0.5369571232846212
Team 4: rating = 0.5349109263288253
Team 1: rating = 0.4288594144453331
Team 3: rating = 0.35096444755792117
Team 2: rating = 0.34416697668415475

Team 5 was the best, followed very closely by team 4.

The temperature near the midpoint of the insulated edge is around 1.83 after 1s

Given a metal bar of length 1 that lies along the unit interval. Its temperature distribution is

$$g(x)=6x^2 - 4x $$

At t=0, its left end is 3 degrees and right end is -3 degrees.

Sketch the distribution at times

$t=0,t=0.01,t=0.1$,and $t=10.$

Looking for the temperature distribution in a steady state problem (i.e. the time derivative is not relevant once the system reaches steady state)

My given equation and boundary values were

$$ u_t = 3u_{xx} + 8, u(0, t) = -4, u(1, t) = 6 $$

when $ u_t = 0 $ the sytem is steady state, then solving for $u_{xx} $gives $ u_{xx} = \frac{8}{3} $

anti-differentiating twice gives the general solution $ u(x) = \frac{8}{3}x^2 + ax + b $

Then, using the boundary values:

$$ u(x) = \frac{4}{3}x^2 + \frac{26}{3}x - 4 $$

The displacement for my particular string set up at t = 1.3s at the midpoint was -.632