Question

Please help me with this 1D vibrating string problem. That has a Dirichlet boundary condition at both ends and the string is at rest when t=0.

Picture on the equation below

htt(t, x)=c2hxx(t, x) + f sin(vt), x E [0, π].

What is missing for this to be solved? Please elaborate

Answer 1

"For 10 vibrating string circlet boundary condition at both ends and string is at test when t = 0 h_tt (t, x) = c^2 h_xx (t, x) + f sin vt, x_0 therefore u_tt = c^2 u_xx U(x, 0) = F(x) therefore we have xT"" = c^2 x"" T T^""/c^2T = x^""/x = K therefore for boundary conditions to x (x) A = 0 B sin (lambda L) = 0 x_n (x) = sin (n(x)/L) n = 1,2,.. therefore f(x) = sigma^q_n = 1 c_n sin (nnx/L) therefore D_n = 2/cn pi integral^L_0 g(x) cos theta dx therefore open boundary condition means no force acts on end of string As tip of string has infinite small mass thus we can say for \r\n static equilibrium forces acting can be analyzed. Force acting in direction of string equals to tension of string partial differential times u = u T Ux/squareroot 1 + x^2 almostequalto T_ux T_UX (6) = integral^6_0 e Utt (c) dx "