Springs are super important in physics. Why? Because we can approximate many things as though they were springs. Also, we can analytically solve for the motion of a mass on a spring.

In general, the magnitude of the force a spring exerts on something can be represented by:

Where k is the spring constant (how stiff the spring is) and s is the amount the spring is stretched.

## Measuring k part 1

Take a spring. Hang it vertically and add weights to it. Make a plot of force vs. stretch. From the slope of this line, you can get the spring constant. Don’t forget about uncertainty.

## Measuring k part 2

One of the cool things about a mass oscillating on a spring is that the period of motion can be found by:

So, this means that you can change the mass on the end of the spring and let the thing oscillate up and down. Record the period and the mass. Change the mass and record the new period. Do this for at LEAST 5 different masses. Use some type of graph such that it is a linear function (I will let you think about what to plot). From this plot, you can determine the spring constant (again).

Which method gives a better result for the spring constant? Why?

You also want to collect position-time data for this oscillating spring. Use the motion detector (set it up below the spring) and get position-time data. You will want to save this so that you can compare it to your vpython model.

## Modeling

Now you will make a vpython model of the spring. The goal is to have the motion in the vpython model agree with your actual real life data. To help you with this program, I uploaded a document to Blackboard.