1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Eigenvalues of a string with fixed ends and a mass in the middle

  1. Apr 6, 2016 #1
    Hi there. First of all, sorry for my bad english. I ´m trying to solve next exercise, from Vibrations and Waves in Continuos Mechanical Systems (Hagedorn, DasGupta): Determine the eigenfrequencies and mode-shapes of transverse vibration of a taut string with fixed ends and a discrete mass in the middle.

    I set next wave equation:

    T * ∂^2 Y/ ∂^2 X = ( ρ + m*δ(x-L/2) ) * ∂^2 Y/ ∂^2 t

    where
    T: tension, ρ: lineal density of the string, m: mass of the particle in the middle of the string, δ: Dirac delta, L: lenght of the string, and the boundary conditions are Y(0,t)=0 and Y(L,t)=0.


    I don`t know how to continue this, because to determine the eigenvalues, I need the wave equation, but it isn`t the usual Y(x,t) = [A*Cos(k*x)+B*Sin(k*x)]*[C*Cos(w*t)+D*Sin(w*t)]. How can I solve this differntial equation? Or another way to solve this?
     
  2. jcsd
  3. Apr 8, 2016 #2
  4. Apr 8, 2016 #3
    Thank you drvrm!!!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Eigenvalues of a string with fixed ends and a mass in the middle
Loading...