Which sets of coefficients aodd aeven bodd and beven are

Question

A string of length L is fixed at both ends. The speed of waves on the string is c. The string is initially displaced a distance h uniformly along its length, and is released from rest at t=0. (The string initially has a very large slope at x=0 and x=L; assume the slope is infinite.)

For ω_n=ck_n=cnΠ/L, the displacement of the string for t≥0 is

y(x,t) = _n-1∑^∞(A_ncosω_nt+B_nsinω_nt)sink_nx

(a) Which sets of coefficients A_odd, A_even, B_odd, and B_even are zero? (b) Determine the values of the nonzero coefficients. Express your results only in terms of c, L, h, and n.