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Total thermal energy from heat equation

  1. Sep 28, 2016 #1
    1. The problem statement, all variables and given/known data
    upload_2016-9-28_19-53-17.png

    2. Relevant equations
    Heat equation

    3. The attempt at a solution
    I can derive E(t) to get integral of du/dt over 0 to L, which is the same as integrating the right hand side of the original equation (d2u/dx2+sin(5t); while this allows me to take care of the d2u/dx2, I don't know what to do with the sin(5t) term or proceed from there.

    Thanks.
     
  2. jcsd
  3. Sep 29, 2016 #2

    Ssnow

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    Gold Member

    Hi, mmm ##\int_{0}^{L}\sin{5t}dx=L\sin{5t}## ...
     
  4. Sep 29, 2016 #3

    Ssnow

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    Gold Member

    Another hint, when you find ##\frac{\partial}{\partial t} E(t)## as a function of ##t## you must integrate in order to find ##E(t)##, this gives you the problem to determine a constant of integration ... you can solve this calculating ##E(0)=\int_{0}^{L}u(x,0)dx=\int_{0}^{L}1+100\sin{\left(\frac{2\pi x}{L}\right)}dx## ...

    Ssnow
     
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