% A beaded string, pinned at both ends and struck near one end. Small and
% fast to run. Its transverse modes are
%   f_k = (1/pi) sqrt(f0/(m a)) sin(k pi / (2(N+1))),
% nearly harmonic for k << N. A hard strike stretches the string, raising
% the tension and with it the pitch while the amplitude is large; the
% string can also swing in y as well as z.

N = 120;           % free beads
L = 0.65;          % length (m)
mu = 2e-3;         % mass per length (kg/m)
T = 60;            % tension (N)
strain = 0.01;     % spring stretch at rest

[pos, E] = bp_chain(N + 2, L);
a = L / (N + 1);
k = T / (strain * a);

sys.pos = pos;
sys.mass = mu * a;
sys.pinned = [1, N + 2];
sys.springs = bp_springs(pos, E, k, T);
sys.dashpots = [E, 2e-4 * ones(size(E, 1), 1)];
sys.friction = 2e-5;

hit.t = 0;
hit.beads = bp_near(pos, [0.12 0 0], 0.01);
hit.force = [0 0.2 1] * 0.8; % N per bead; slightly off-axis
hit.duration = 1.5e-3;
sys.hits = hit;

sys.listen = struct('beads', N, 'dir', [0 0 1]);
sys.duration = 2.5;

fprintf('fundamental (small amplitude): %.1f Hz\n', sqrt(T / mu) / (2 * L));