This page briefly describes how to use this tool to solve Newton's Second Law numerically and produce either a table or a graph of the results. The particular example used is a one-dimensional simple harmonic oscillator, an example of which would be a mass on a spring.
While using the tool, click on any blue link to learn more about a a particular subject.
Acceleration Panel
If you have not already launched the Newton Tool by clicking the Launch Newton Tool button on the main page, you may do so here. The panel shown below will appear.
For this beginning tutorial, we'll walk through the default one dimensional problem. Because our problem will only have one dimension, namely x, the first field has a 1 in it. Next, you should enter the acceleration equation of the problem you are interested in. This should be the right hand side of an equation of the form: a=f(x,vx,t). By default the acceleration equation describes a simple harmonic oscillator. In your equation, be sure to use x as the position variable and vx as the velocity of that variable.
Most mathematical operations are allowed. Here is a list of common mathematical functions that work with this tool.
Enter your acceleration equation. In the present case, since we are following the default problem, you need not change the acceleration. Click 'Next' in order or click on 'Initial Conditions' in the Task Bar to proceed to the next step.
Initial Conditions
In this panel you should enter what you would like the initial conditions to be for your problem and a couple of other parameters. The first row is where you input your initial position and velocity as shown below.
Here, leave the initial position and velocity at their default values of 1.7 and 0 respectively.
The next two entries are the final time and the adaptive step factor. The final time is the model time at which the calculation stops. By default, the time begins at t=0, so you may need to translate your equation in time if you are interested in another time range. For the present case, leave the Final Time at the default value 90.
The adaptive step size is a bit more difficult to explain. The goal is to make your graphs look smooth. If any plots you create do not look smooth, decrease the adaptive step size from 1. to a smaller value, like 0.01. On the other hand, if there are far too many points in your graph, increase this number, for example, to 100, to decrease the number of points. For the present calculation, leave the Adaptive step factor at 1. For more information about the adaptive step size, see the Overview under Technical Resources in the left hand column of links.
Once you are confident your equation and initial conditions are correct, click 'Calculate' to proceed. This runs the calculation and then gives you access to the 'Plot Results' and 'Table' panels. Click the panel you desire on the left or click next to proceed.
Plot Results
'Plot Results' allows you to plot any combinations of your results. Simply select which parameter you would like to be along the x axis, and which you'd like to be along the y axis.
For most plots, the axis types may be left to linear. Also, the mins and maxs may be left to default.
Select the parameters you would like to plot. For the present case, choose x position vs time. Now, click 'View Plot' to see your results!
The results are opened in a new window.
Notice the 'View data' button. This will display a list of all values used to make this plot in an easy to read html table.
Table
The last panel allows you to output any data you want as a table. This can either be done as an html table (much like above) or as an ASCII table that can easily be imported into other data programs.
Select the parameters you would like entered in the table and select which kind of table you would prefer. For the present calculation, check Time and x_pos and then click View HTML Table.
An example of an html table is given below.
An example of an ASCII table is given below.
Challenge
Try making a plot of x velocity versus time. Leave the plot panel up. Now go back to the Acceleration Equations(s) task page and try running the calculation with a spring constant twice as large, that is, with an acceleration -4.0*x. Then plot x velocity versus time. If you left the plot panel up, you can use the back and forward button to compare the two plots.
