Science Buddies: "Ask an Expert"

I am having some difficulty trying to conduct my experiment on Hooke's Law. My experiment, in its simplest form, is I wish to determine if an object whether a greater or less mass has a higher or less oscillation. I created this project based on these two other projects I found on the Science Buddies Project ideas, " Simple Harmonic Motion in a Spring-Mass System," and "Applying Hooke's Law: Make Your Own Spring Scale." The problem is I don't know how to calculate this project mathematically. I followed the Simple Harmonic Motion in a Spring-Mass System procedures but got lost after period 5, reading it three times already. If anybody could help comprehend this information without all that complicated math it would be a huge help. Sorry if I sound a little stupid, but I recently entered high school and don't know much on physics, though i am interested in it. Also, if anybody could provide some good project idea names that would be much appreciated.

~Charlie

Hello ProdigyGenius,

Welcome to the forum.

The procedure for the “Simple Harmonic Motion in a Spring-Mass System” does include quite a few calculations and I can see how it might be easy to get lost!

The basic concept here is to use Hooke's Law to calculate a spring constant from the oscillation periods found for different masses attached to the spring. In this experiment, there are two unknowns: the spring constant (k) and the effective mass of the spring (labelled me in the procedure). A graphical method is used to find both unknowns. Mass added to the spring is plotted against the square of the oscillation period (T2/4pi2). The slope of the line formed from the data can be used to calculate the spring constant. The intercept of the line (where the line crosses the y-axis) is the effective mass of the spring.

Step 5 in the procedure is all about converting the oscillations you found in your experiment to the data used for the graph (T2/4pi2). The values for T are in seconds per oscillation. But in your experiment you counted the number of oscillations per minute. Therefore you must make a conversion of your data.

The first step is to convert from oscillations per minute to oscillations per second. To do this you divide your counts by 60 (seconds per minute). This is shown in column C of the table in step 5.

Next, you must convert from oscillations per second to seconds per oscillation (this is the T in the Hooke's Law equation). To do this you divide 1 by the oscillations per second from the previous step. This is shown in column D of the table in step 5.

Finally, you use the seconds per oscillation (T) from the previous step to calculate T2/4pi2. To do this you square the T values and divide by 4 times pi squared. This is shown in column E of the table in step 5.

If you carefully follow these steps you'll have your data in the form needed to make the graph and to calculate the spring constant and effective mass. The remaining steps in the procedure are all about these calculations.


I hope this helps. Please ask again if you have more questions.

A. Norman

Wow very helpful, but can you check if this statement is correct. The effective mass of the spring is basically how much mass the spring can take before breaking and not applying to Hooke's Law. Yes or no? Also, my project is supposed to be testable and measurable with an independent and dependent variable, so would this project work?

ProdigyGenius,

First, the effective mass of a spring is not the amount of mass it can take before breaking. In a mass-spring system, the spring has a non-negligible mass that contributes to the motion. However, since not all of the spring is in motion it is some value less than the actual total mass of the spring. In a theoretical ideal spring the effective mass is 1/3 the total mass of the spring. For your case, as mentioned above, where your data graph crosses the Y axis is the effective mass.

Second, an independent variable is one you change, whilst a dependent variable will change based on changes to the independent variable. From your hypothesis above your independent variable is the mass you add to the spring and your dependent variable is the greater or less oscillation.

So I simply don't have to do all that math, but how do I apply this project to Hooke's Law since one of the requirements of my project is to relate it to a scientific law or principle and real-life scenario.

ProdigyGenius,

According to Hooke's Law, the time for an oscillation of a spring (the oscillation period) is proportional to the mass attached to the spring. Based on your project description, your experiment is a demonstration of Hooke's Law in action.

I think that the math part is up to you. That is, you could have an experiment that demonstrates Hooke's Law without any math. For example, you could take pictures of your spring with different masses attached to show the different amounts of displacement (stretch) of the spring. But including the math would make your project more sophisticated.

Good luck with your project. Please post again if you have more questions.

A. Norman