% giant ass calculator for ENGN 310 design calcs

%input parameters
w_in = .5;
l_in = 8;
t_in = .187;
m = 6;

width = w_in * 0.0254;
l = l_in * 0.0254;
t = t_in * 0.0254;

% i) for k
I = (width*(t^3))/12;
E = 3.2*10^6;
k = (3*E*I)/l^3

% ii) tobias has in his tiny notebook
w0 =  736.44 ; %rad/s

% ii) critical value for de (at pull-in length)
% eq: k = 2.7/de^(1+2.7) ==>
decrit = (2.7/k)^(1/3.7) % in cm

% iii) know operating de is twice decrit
de = decrit*2;
ke = 2.7/de^(3.7)
c = 1;

wm = ((k - ke)/m)^(1/2)
% max amp occurs at wm
max_amp = ((1+((2*c*wm)/w0)^2)^(1/2))/((1- (wm^2/w0^2))^2 + (2*c*wm/w0)^2)^(1/2)