Vibrations problem - Transverse in a string under tension

[alexisonsmith]

Homework Statement

A cord of length L density p and cross-sectional area S is under tension T with the left end fixed and the right end attached to a spring-mass sstem. Show that the equation for the natural frequencies is given by:

tan(wL/c) = -(T/kL)((wL/c)/(1-(w/w_n)^2))

Homework Equations

w_n^2 = k/m and c^2 = T/(pS)

The Attempt at a Solution

I have tried this but I am really having problems starting this problem out, please help

 

[ideasrule]

Are you sure that equation is right? The natural frequencies are given very simply by f=v/lambda, where v^2=c^2 = T/(pS) and lambda is a half-integer multiple of the pipe's length.

 

[alexisonsmith]

Yes it is Q.2 on the sheet which I have attached.