# Physics Lab

Dominic Stone

Lab Partner: Andrew Lugliani

January 9, 2012

Physics 132 Lab

Section 13

Theory For this experiment we investigated and learned about simple harmonic motion. To do this we hung and measured different masses on a spring-mass system to calculate the force constant k. Simple harmonic motion is a special type of periodic motion. It is best described as an oscillation motion that causes an object to move back-and-forth in response to a restoring force given by Hooke’s Law:

1) F=-kx

Where k is the force constant. Then using two different procedures, we calculate the value of the force constant k of a spring in our oscillating system. We observed the period of oscillation and use this formula:

2) T=2(m/k)

Then we reduced the equation to solve for the value of k by:

3) k=4^2/slope

“Slope” represents the slope of the graph in procedure B. k is then the measure of the stiffness of the spring. We can then compare k to that of a vertically stretched spring with various masses M. By using the following equation:

4) Mg=kx

Where x is the distance of the stretch in the spring. To find the value of the constant k we take the data from procedure A and graph it. Using this graph, we use equation:

5) k=g/slope

We can compare the two values of the constant k. Both values should be exact since we used the same spring in both procedures. Here simple harmonic motion is used to calculate the restoring force of the spring-mass system.

Procedure

Part A:

First, we set up the experiment by suspending the spring from the support mount and measured the distance from the lower end of the spring to the floor. After, we hung 100 grams from the spring and measured the new distance created from the stretch of the spring. We then repeated this step for masses 200 to 1000 grams, by increasing the weight by 200 grams each time. Then we took this data and plotted them on a graph with