Find the Total Energy of the String

[Aerimiel]

Homework Statement

Hello everyone!
Would you be so kind as to give me an advise for the following problem:

Find the total energy of a vibration of the string oscillating with nth normal mode with amplitude A. The tension in the string is T and its total mass is M.

Relevant Equations

ψ(x,t) =∑Asin(kx)sin(ωt)

Steps that I've taken:

• First, compute the derivative of the psi-function with respect to time and then take the square of the result
• Second, input the result into the KE integration formula.
• All that is left is to find the integrand, however this is where calculations became really "messy". It seems that I have to find the time t at which the PE is zero. However, I keep on getting the wrong result.

Thank you very much for your attention!

 

[Orodruin]

Please show the computations of your attempt (type it out, do not attach photos) and be specific in where you run into trouble. If you do not do that it is impossible to pinpoint exactly what your issue is. For example, ”messy” carries very little actual information.