Euler-Cromer method

Python Help
1

I am an absolute beginner to programming and I have to make a program that numerically calculates the speed and position as functions of time by using the Euler-Cromer method stooping when the brick stops and find out how far it moves. Furthermore, I am asked to use matplotlib to plot the results and show of graphs for position, speed and acceleration as functions of time, but I have no idea where to even begin.

2

There are several guides online for Euler’s (and related) methods. Here is one that covers Euler-Cromer

https://cooperrc.github.io/computational-mechanics/module_03/03_Get_Oscillations.html

3

Hi,

You will have to learn how to start using for loops since this type of problem requires multiple iterations (you can also use list comprehensions which is ideally built for this). For example, when you plot a function, you plug in multiple values of the independent variable into a function. For each value of say, x, there is a corresponding value of y. You then connect the dots in the graph, and you now have a plot. However, to do this in Python code to do it for you, you can follow this example to familiarize yourself with the concepts to get you started.

Say, the values of x are: x_values = [2, 3, 4, 5, 6] (the independent variable values)

The function is: y(x) = x ** 2 + 5 * x - 1.25 (the dependent variable values)

To solve for y, you perform the following:

y_values = [ x ** 2 + 5 * x - 1.25 for x in x_values]

To plot on a graph the x_values vs. y_values:

from matplotlib import pyplot as pl

x_values = [2, 3, 4, 5, 6]

# Using a list comprehension to obtain values
y_values = [ x ** 2 + 5 * x - 1.25 for x in x_values]

print(y_values)

pl.plot(x_values, y_values, 'r')

pl.xlabel('X-Value')
pl.ylabel('Y-Value')
pl.title('Plot of X vs. Y')

pl.show()

What you’ll be doing is basically the same idea/concept.

Try learning the fundamentals first.