A string is stretched to a tension T and its ends x = 0 and x = L are

attached to rings of mass M which are free to slide on parallel smooth

wires which are perpendicular to the string. Show that the transverse

displacement must satisfy the conditions

My_tt = Ty_x at x = 0 and My_tt = −Ty_x at x = L,

and that the normal frequencies are the numbers w/2pi, where

cot(wl/c) = T/2Mwc ((Mwc/T)^2 - 1)

I have spent a good few hours going over this and I cant seem to get it right!

using sepeation of variables I have that y(x,t) = sin npix/l(cos(npict/l) + sin(npict/l)

but then when I differentiate these and put them in for the initial conditions I cant seem to get anywhere!

many thanks