Hello,

I am currently trying to solve the 1D wave equation for longitudinal waves in a cantilever (BOUN2) with an endmass (BOUN1). The entire system is at rest (INIT1) and is excited with an initial velocity at t=0 at the free end (INIT2). I am unable to generate a solution. With simpler boundary conditions the system is solvable here i am getting the error that INIT2 is not specified on the boundary of the domain. This should yield a fourier series. Could someone help me with the proper definition of the boundary?

   c=1;
   k=1;
   L=1;
   v=1;
   BOUN1= k*Derivative[0, 2][u][L, t] + Derivative[1, 0][u][L, t] == 0;
   BOUN2= u[0, t] == 0;
   INIT1= u[x, 0] == 0;
   INIT2 = Derivative[0, 1][u][L, 0] == -v ;
   DEQN1 = D[u[x, t], {x, 2}] - c*D[u[x, t], {t, 2}] == 0;
   solution1= 
   NDSolveValue[{DEQN1, BOUN1, BOUN2, INIT1, INIT2 }, u, {x, 0, L}, {t, 0, 0.00019}]
   Plot[solution1[L, t], {t, 0, 0.00019}, PlotRange -> All]