05_curve_fitting

Problem 2

Coefficient of Determination

Part A: 0.9801
Part B: 0.9112
Part C: 0.9462
Part D: 0.9219

Best Fit Lines

Part A

y = 0.375+0.98644x+0.84564/x

Part B

y = 22.47-1.36x+0.28x^2

Part C

y = 4.0046e^(-1.5x)+2.9213e^(-0.3x)+1.5647e^(-0.05x)

Part D

y = 0.99sin(t)+0.5sin(3t)

Problem 3

Part A

darts = dlmread('compiled_data.csv',',',1,0);
x_darts =darts(:,2).*cosd(darts(:,3));
y_darts =darts(:,2).*sind(darts(:,3));

ur = darts(:,1);
i = 1;

for r = 0:32
    i_interest = find(ur==r);
    mx_ur(i)= mean(x_darts(i_interest));
    my_ur(i)= mean(y_darts(i_interest));
    i = i +1;
end
    accuracy = mx_ur + my_ur;
    val = 0; %value trying to be closest to
    abs_accuracy = abs(accuracy-val); %takes absolute value of accuracy vector
    [~, index] = min(abs_accuracy)
    closest_value = accuracy(index)

The most accurate dart thrower was person 31, with a combined x and y average of 0.0044 cm away from zero.

Part B

darts = dlmread('compiled_data.csv',',',1,0);
x_darts =darts(:,2).*cosd(darts(:,3));
y_darts =darts(:,2).*sind(darts(:,3));

ur = darts(:,1);
i = 1;

for r = 0:32
    i_interest = find(ur==r);
    stdx_ur(i)= std(x_darts(i_interest));
    stdy_ur(i)= std(y_darts(i_interest));
    i = i +1;
end
    precision = stdx_ur + stdy_ur;
    val = 0; %value trying to be closest to
    abs_accuracy = abs(precision-val); %takes absolute value of accuracy vector
    [~, index] = min(abs_accuracy)
    closest_value = precision(index)

The most precise dart thrower was person 32, with a combined x and y standard deviation of 3.407.

Problem 4

Part A

function [mean_buckle_load,std_buckle_load]=buckle_monte_carlo(E,r_mean,r_std,L_mean,L_std)
    r= normrnd(r_mean,r_std,[100 1]);
    L= normrnd(L_mean,L_std,[100 1]);
    p_cr = (pi.^3.*E.*r.^4)./(16.*L.^2);
    mean_buckle_load = mean(p_cr);
    std_buckle_load = std(p_cr);
end

Output:

Mean_buckle_load = 160.81 N
Std_buckle_load = 70.21 N

Part B

N=100;
r_mean=0.01;
r_std=.001;
p_cr = 160.81; %N - from part A
r=normrnd(r_mean,r_std,[N,1]);
L = ((pi^3*E.*r.^4)./(16*p_cr)).^0.5;
L_mean = mean(L)

Output:

Length (L) = 4.955 m

Problem 5

Part A

cd_out_linear = sphere_drag(300,'linear') = 0.1750
cd_out_spline = sphere_drag(300,'spline') = 0.1809
cd_out_pchip = sphere_drag(300,'pchip') = 0.1807

Part B

Problem 6

Method	Value	Error
Analytical	8.375	0%
1 Gauss Point	8.229	1.74%
2 Gauss Point	8.375	0%
3 Gauss Point	8.375	0%

cpl11001/05_curve_fitting

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