Maybe you know I like numerical calculations, well I do. I think they are swell. [VPython](http://vpython.org) is my tool of choice. In the post [Basics: Numerical Calculations](http://blog.dotphys.net/2008/10/basics-numerical-calculations/) I used vpython and excel to do something simple. I will do that again today (in that this problem could also be solved analytically). However, there is one big difference. This problem has a non-constant forces. Suppose I have a mass that is connected by a spring to a wall. This mass-spring is sitting on a table with no friction.

![Screenshot 27](http://blog.dotphys.net/wp-content/uploads/2008/10/screenshot-272.jpg)

There is a very interesting property of springs. The more you stretch them, the greater the force they exert (in the usual model of springs). This model works very well.

![Screenshot 28](http://blog.dotphys.net/wp-content/uploads/2008/10/screenshot-282.jpg)

This is known as Hooke’s law. I have written it as a scalar for simplicity. The “k” is called the spring constant. It is a measure of how “stiff” the spring is. The value “s” is the amount the spring is stretched. Typically, there is a minus sign in front of the ks to indicate that the force is in the opposite direction that the spring is stretched. Really, in a scalar equation this is rather silly to include (but everyone does anyway).

**Question: What will the motion of the mass be like if I pull it back and then let go?**

Although this can be determined analytically, I am going to first calculate this with vpython. I will try to show all the details so that you can reproduce this also. If you have not already installed [vpython](http://vpython.org), do that now (don’t cost nothing).