**INTRODUCTION:**

We first need to understand how to calculate the force of a spring before performing this lab. We look at Hooke's Law which can be described as a spring stretched a distance, x, from its equilibrium position will exert a restoring force that is directly proportional to the distance. The force can be written as:

F = -kx

where k is the spring constant and depends on the stiffness of the spring. The minus sign means that the Force is opposite the direction of the displacement of the spring.

When a mass hangs from a spring, is stretched, and let go, it will oscillate about the equilibrium point of when the mass hangs. From Newton's Second Law and with calculus we can find the period, T (in seconds), from the equation:

where m is the mass supported by the spring |

Now that we know what our equations we are going to be working with, we need to see where we are going to get these values from:

**PROCEDURE:**

To begin this lab, we will first need to gather the proper materials:

- spring
- masses
- weight hanger
- meter stick
- support stand with clamps
- motion detector
- Lab Pro Interface
- wire basket

We set up our support rods the same way as the picture above and set the motion detector directly underneath the hanging spring inside the wire basket to protect the detector. We hung the spring on the rod and measured how high off the ground the bottom of the spring was.We hung a 350 g mass on the spring and measured how far the bottom of the spring was from the ground with the meter stick. We found the difference in the length of the spring and recorded the value. We then did it for 450 g, 550 g, 650 g, 750 g, 850 g, 950 g, and 1050 g. We then calculated the normal force of the masses which is equal to the weight force since the (Fnet)y was 0. We will use these values to find the spring constant, k, with the equation:

k = F/-x

With these values we were able to make a graph and were able to solve for k doing a linear fit since the k value is the slope.

Next, we opened up the file Hooke's Law in Logger Pro because now we are going to stretch the spring with a mass, in equilibrium, 10 cm and allow it to oscillate. We recorded the position of the oscillating mass with the motion detector and allowed it to oscillate for 10 seconds. This gives us the time necessary to perform 5 cycles because in this part of the lab we will be finding an average time, T (sec), per period of the oscillation. We first hung 350 g on the spring and then stretched it 10 cm down and let it go and run for 10 seconds. We then performed this test for all the same masses used in the previous test.

With the information obtained above, we were able to make a T^2 vs mass graph.

**CONCLUSIONS:**

In this lab I learned how we could find the spring constant of a spring from 1. Hanging a mass and measuring the displacement of the spring and 2. Having a mass oscillate on the spring.

One factor that could have caused a difference in our values for k is that the oscillating mass could have lost some potential energy causing the spring to oscillate slower. We can further study spring constants by studying a spring that compresses and finding its constant.