function P = plate_setup(params)
% PLATE_SETUP  Constants derived from the parameters, shared by both methods.
%
%   P = plate_setup(params) copies params and adds
%     D                    bending rigidity E h^3 / (12 (1 - nu^2))       [N m]
%     hole_area            area of the suspension hole                     [m^2]
%     hole_x, hole_y       the hole, on the centreline near the top edge   [m]
%     plate_mass           rho h (W H - hole area)                         [kg]
%     g                    standard gravity                                [m/s^2]
%     thread_k             transverse spring of the thread at the hole,
%                          m g / L: the linearized pendulum, not a clamp   [N/m]
%     critical_frequency   coincidence frequency c^2 / (2 pi) sqrt(rho h / D),
%                          below which a small unbaffled plate radiates
%                          inefficiently                                   [Hz]
%     f_max                highest mode kept, 0.47 fs                      [Hz]
%     Kb, Ks               surface-stress factors E h / (2 (1 - nu^2)) and
%                          E h / (2 (1 + nu)) (plate_stress)               [Pa m]
%     hertz                the contact constants (plate_hertz)
%
%   Coordinates are measured from the plate's centre, x to the right and
%   y towards the threaded top edge, as in the simulators this lab follows.

P = params;
pl = params.plate;
mat = params.material;
P.D = mat.E * pl.thickness^3 / (12 * (1 - mat.nu^2));
P.hole_area = pi * (params.hole.diameter / 2)^2;
P.hole_x = 0;
P.hole_y = pl.height / 2 - params.hole.edge_offset;
P.plate_mass = mat.rho * pl.thickness * (pl.width * pl.height - P.hole_area);
P.g = 9.80665;
P.thread_k = P.plate_mass * P.g / params.thread.length;
P.critical_frequency = params.mic.sound_speed^2 / (2 * pi) * sqrt(mat.rho * pl.thickness / P.D);
P.f_max = 0.47 * params.render.fs;
P.Kb = mat.E * pl.thickness / (2 * (1 - mat.nu^2));
P.Ks = mat.E * pl.thickness / (2 * (1 + mat.nu));
P.hertz = plate_hertz(params);
end