Physics Lab: You Don’t Understand Simple Harmonic Motion Unless You Can Model It

If you just collect experimental data, you are a collector. If you just make models, you are a philosopher. It is the scientist that makes models and compares them to real data. So, let’s do that.

We are going to collect position data for a mass connected to a spring (simple harmonic motion) and them model it with a numerical calculation in python. It turns out that a mass on a spring shows up in a bunch of different places in physics — it’s also not quite so trivial. The following is a lab-based activity that pretty much any physics student in an introductory course could create.

Force Due to A Spring

Let’s start off by considering an ideal spring. When you pull on a spring, it will exert a force (Fs) in the opposite direction as the stretch. AND…the magnitude of this spring force increases with the stretch distance (s). We can model this ideal spring force with Hooke’s Law:

Here k is the spring constant (in Newtons per meter) — a measure of the “stiffness” of the spring. Oh, you think there should be a negative sign in there? Well, this is a magnitude equation (no arrows over the force and stretch). The magnitude of a force is always positive. OK, I get where you are coming from though. You want the negative sign to…