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My matrix was matrix = [ [0,2,4,1,1], [1,0,3,2,1], [3,4,0,1,2], [1,3,3,0,4], [4,3,1,4,0] ] The eigen ranking was: Team 5: rating = 0.5351649756702808 Team 4: rating = 0.516996248452163 Team 3: rating = 0.43493231817629663 Team 1: rating = 0.3710347855055461 Team 2: rating = 0.3456593618764917 Team 5 was the best team.
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Given the conditions of my problem with $\kappa=0$ and $f=0$ the temperature at the lower right hand corner of the bar at steady state is 0.75700.
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The temperature of the midpoint at the insulated edge at t=1s is 0.16587 as shown in the image below.
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A metal bar of length 1 with a temperature distribution given by: $$g(x)=3x^2-1x.$$ At $t=0$ its left end is set to temperature -2 and its right end to 3. Sketch the temperature distribution at time t=0, t=0.01, t=0.1, and t=10.
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Heat flow with a constant internal heat source is governed by: $$u_t=1u_{xx}+3, u(0,t)=1, u(1,t)=2.$$ Since this is a steady state temperature distribution, $u(t)=0$ since $u(x,t)$ does not change with time. Thus, $$1u_{xx}+3=0.$$ Solving for $u_{xx}$ yields $u_{xx}=-3$. Integrating this twice with provide the result,…
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The displacement of the midpoint from equilibrium at time t=1.9s is -0.028.