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Vibrating string

  1. May 25, 2012 #1
    1. The problem statement, all variables and given/known data

    (∂^2 u)/(∂t^2 )=a^2 (∂^2 u)/(∂x^2 ) x∈(0,l) t>0
    u(0,t)=0 ; ∂u/∂x(L,t)=0
    u(x,o)=u1; ∂u/∂t(x,o)=x

    I can not figure out physical interpretation of boundary condition ∂u/∂x(L,t)=0, what does it mean. Can someone can help me with this ?
    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 25, 2012 #2
    The string is clamped at L and 0. So its amplitude is 0 there.
     
  4. May 25, 2012 #3
    That's not true. ∂u/∂x(L,t)=0 means that the string is always perpendicular to the wall at the other endpoint. So you can think a very relaxed string being attached to a pole, sliding along it without friction.
     
  5. May 25, 2012 #4
    Thanks.
     
  6. May 25, 2012 #5
    One way to understand what is it each time, is:
    1. Know what derivatives in your problem mean.
    2. See how it affects your solution after you bring them in it.
     
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