05_curve_fitting

Question 2

function [a,fx,r2]=least_squares(Z,y)
% least squares solution for input matrix Z and measurements y
% outputs are:
% a: constants for best-fit function
% fx: function evaluations at xi
% r2: coefficient of determination

a = Z \ y;
fx = Z * a;
e = y - fx;
Sr = std(e);
St = std(y);
r2 = 1 - Sr/St;
end

Coefficient of Determination

• 0.9801
• 0.9112
• 0.9462
• 0.9219

Part A

• a = 0.3745 0.9864 0.8456 \

Part B

• a = 22.4669 1.3627 0.2763 \

Part C

• a = 4.0046 2.9213 1.5647 \

Part D

• a = 0.9973 0.5025 \

Question 3

• A, Thrower# 31

• B, Thrower# 32

Question 4

function [mean_buckle_load,std_buckle_load,L_mean]=buckle_monte_carlo(E,r_mean,r_std,L_mean,L_std)
N=100;
r = normrnd(r_mean,r_std,[N,1]);
L = normrnd(L_mean,L_std,[N,1]);

Pcr = (pi.^3 .* E .* r.^4) ./ (16 .* L.^2);
mean_buckle_load = mean(Pcr);
std_buckle_load = std(Pcr);

P_test=1000*9.81/100;
sum(2.5<P_test)
L = ((pi^3*E.*r.^4)./(16*Pcr)).^0.5;
L_mean = mean(L)
end

• A, mean_buckle_load = 176.0834 std_buckle_load = 83.7155

• B, L = 30.5858m

Question 5

function [Cd_out]=sphere_drag(Re_in,spline_type)
data = [2	0.52
5.8	0.52
16.8	0.52
27.2	0.5
29.9	0.49
33.9	0.44
36.3	0.18
40	0.074
46	0.067
60	0.08
100	0.12
200	0.16
400	0.19];

Cd_out = interp1(data(:,1),data(:,2),Re_in,spline_type);
end

Part B \

Question 6

method	value	error
analytical	8.3750	0%
1 Gauss Point	8.2292	1.74%
2 Gauss Point	8.3750	0%
3 Gauss Point	8.3750	0%