Plot the slope of a parabola with only the data points being known

Deflection (in meters)

The deflection is given in the following line. The data was acquired experimentally.

Thus, no equation is available.

x = linspace(-0.5,0.5,25); %length in (meters)
def_3mm_no_grav = -[0.00 5.82e-1 1.08 1.53 1.94 2.30 2.62 2.89 3.12 3.29 3.41 3.49 3.51 3.49 3.41 3.29 3.12 2.89 2.62 2.30 1.94 1.53 1.08 5.82e-1 0.0]*(10^(-3));

Slope

I tried using polyfit, but I'm not that familiar with the function so I could be using it wrong

slope_3_no_grav = polyfit(x,def_3mm_no_grav,1)

How should I go about acquiring the values/ equation of the slope in order to plot it?

Answer 1

[Alan Stevens]

Like this?

x = linspace(-0.5,0.5,25); %length in (meters)
def_3mm_no_grav = -[0.00 5.82e-1 1.08 1.53 1.94 2.30 2.62 2.89 3.12 ...
    3.29 3.41 3.49 3.51 3.49 3.41 3.29 3.12 2.89 2.62 2.30 1.94 1.53 ...
    1.08 5.82e-1 0.0]*(10^(-3));
coeffs = polyfit(x,def_3mm_no_grav,2);  
fit_3mm_no_grav = polyval(coeffs,x);
slope_coeffs = [2*coeffs(1) coeffs(2)];
slope_fit = polyval(slope_coeffs,x);

plot(x,def_3mm_no_grav,'o',x,fit_3mm_no_grav),grid
legend('data','curve fit')
xlabel('x'), ylabel('3mm no grav')

figure
plot(x,slope_fit),grid
xlabel('x'), ylabel('slope of 3mm no grav')

[Ludwig Crous]

Thank you so much.

It is greatly appreciated.

Answer 2

[Ive J]

Before fitting, it's a good practice to visualize your data to better understand the rough relationship between your variables. In your case, a 2nd order polynomial function seems a reasonable choice:

x = linspace(-0.5,0.5,25); %length in (meters)
y = -[0.00 5.82e-1 1.08 1.53 1.94 2.30 2.62 2.89 3.12 3.29 3.41 3.49 3.51 3.49 3.41 3.29 3.12 2.89 2.62 2.30 1.94 1.53 1.08 5.82e-1 0.0]*(10^(-3));

% fit a curve 
coef = polyfit(x, y, 2); % equation would be f(x) = coef(1)*x^2 + coef(2)*x + coef(3)

% now draw the fit
newx = linspace(min(x), max(x), 100);
newy = polyval(coef, newx); 
plot(x, y, 'o', newx, newy, 'linewidth', 1.5)

[Ludwig Crous]

Thank you.

Answer 3

[Sargondjani]

clc;

clear all;

close all;

x = linspace(-0.5,0.5,25); %length in (meters)

def_3mm_no_grav = -[0.00 5.82e-1 1.08 1.53 1.94 2.30 2.62 2.89 3.12 3.29 3.41 3.49 3.51 3.49 3.41 3.29 3.12 2.89 2.62 2.30 1.94 1.53 1.08 5.82e-1 0.0]*(10^(-3));

pp=polyfit(x,def_3mm_no_grav,2);% fit polynomial

p_prime = polyder(pp);%take derivative of this polynomial

plot(x,def_3mm_no_grav,'LineWidth',1.5);%data

hold all;

x_acc = linspace(x(1),x(end),1000);

y_acc = polyval(pp,x_acc);

plot(x_acc,y_acc,'--','LineWidth',1.5);%fitted polynomial

%First order approximation around x1:

x1 = 0.1;

y1 = polyval(pp,x1);%function value;

slope_x1 = polyval(p_prime,x1);%slope at x1

x_dev = -0.1:0.01:0.1;

y_slope = y1+ slope_x1*x_dev;

plot(x1 + x_dev,y_slope,':','LineWidth',1.5)

legend('Data','Fitted poly.','First order approx.')