Newton's Second Law Lab

Readme.md

Newton's Second Law Lab Code

This is for a physics paper I wrote. It just generates a model and graph. Although I am writing this for academia, the code does not count towards credit for the paper. Therefore, I release secondlaw.m and convert-units.js into the public domain. Apologies for the messy code.

To run:

octave --no-gui secondlaw.m

secondlaw2.txt is generated from the shell command ./csv-convert.js < secondlaw.txt > secondlaw2.txt.

convert-units.js

#!/usr/bin/env node

/**
 * Converts a comma and newline delimited table of [kg s] to [N m/s^2],
 * assuming that deltaX = 0.500 m and v_initial = 0. 
 * 
 * Takes in input through STDIN and writes to STDOUT
 * 
 * @author Jason Zhao <jason@codesmoothie.com>
 * Date:   2017 October 12
 * @license: public domain
 */

const fs=require('fs');
const input = fs.readFileSync('/dev/stdin').toString()

const print = (a) => {
  console.log(typeof a + ': ' + a);
  return a;
};

const result = input.split('\n').filter(l => l.match(/\S+/))
  .map(line => line.split(',').map(Number))
  .map(line => [line[0] * 9.8, 0.988533017 / Math.pow(line[1], 2.0) ])
  .map(line => line.map(n => n.toFixed(4)).join(','))
  .join('\n')

console.log(result)

image.jpg

Newtons-Second-Law-Lab-Code

Newton's Second Law Lab Code

secondlaw.m

% @author Jason Zhao <jason@codesmoothie.com>
% Date:   2017 Oct 12
% @license: public domain
1;

function theta = normal_equation(X,y)
  theta = (pinv(X'*X))*X'*y
end


data = load('secondlaw3-force-vs-accel.txt');
x = data(:,1);
y = data(:,2);

% X = [x.^2, x, ones(length(x), 1)]
X = [x]
theta = normal_equation(X, y)

% function a = model(b) 
%   a = b * sin
% end


x_1 = 0:0.01:30;
% y_1 = eval(['@(x) ', strrep(
%     strrep(
%       strrep('a*x.^2 + b*x + c', 'a', num2str(theta(1))), 
%       'b', 
%       num2str(theta(2))
%     ),
%     'c',
%     num2str(theta(3))
%   )
% ]);

y_1 = eval(['@(x) ', strrep('a * x', 'a', num2str(theta))])

printf (func2str(y_1))

ylabel('Acceleration (m/s\^2)');
xlabel('Net Force (N)');

hold on;
axis([0 6 0 10])
plot(x, y, 'rx;Data Points;');
plot(x_1, y_1(x_1), '-;Regression;')
% plot(x, y, 'rx');
% plot(x_1, y_1(x_1), '-')
print -djpg image.jpg

pause;

secondlaw.txt

0.050,1.0178
0.100,0.7343
0.150,0.6115
0.200,0.5608
0.550,0.4280
0.300,0.4713
0.400,0.4547

secondlaw2.txt

0.4900,0.9653
0.9800,1.8546
1.4700,2.6743
1.9600,3.1797
5.3900,5.4590
2.9400,4.5020
3.9200,4.8367

secondlaw3-force-vs-accel.txt

0.4900,0.6534
0.9800,1.2368
1.4700,1.8601
1.9600,2.3112
2.4500,2.9589
2.9400,3.4537
3.4300,4.0508
3.9200,4.6515
4.4100,4.7126
4.9000,5.6849

secondlaw3-massHook-vs-Time.txt

0.050,1.230
0.100,0.894
0.150,0.729
0.200,0.654
0.250,0.578
0.300,0.535
0.350,0.494
0.400,0.461
0.450,0.458
0.500,0.417