Physics 116 Lab

Energy in Simple Harmonic Motion

Text Reference: Haliday, Resnick, Walker Section 8.4, 8.5, 15.3, 15.4

Oscillation is essentially movement of an object back and forth.  When the motion repeats at regular time intervals and the same amplitude, the motion is called simple harmonic motion.  We will be examining the simple harmonic motion of a mass on a spring in lab. We can describe an oscillating mass in terms of its position, velocity, and acceleration as a function of time. We can also describe the system from an energy perspective. In this experiment, you will measure the position and velocity as a function of time for an oscillating mass and spring system, and from those data, plot the kinetic, potential and total energies of the oscillating system. Think about how you would expect position and velocity (and therefore potential and kinetic energy) to vary with time.

Pre-Lab Questions

1. What are the expressions a) or PE, b) for KE and c) for total E for a mass on a spring? These should be written in terms of position, speed, and any constants.

2. What are the constants that we will need to determine for the lab?

3. When there are no other forces experienced by the system, what does the principle of conservation of energy tells us about the sum KE + PE?

1. On the web, find the PhET Masses on Springs. Start the simulation (choose experiment mode), make sure that you are doing the experiment "on Earth". 

2. Add a 100 g mass to the spring. Note that in this lab, we will assume frictionless springs at first, until the last, total energy question. So in order to study a frictionless spring, you can move the slider to "none" for damping. In order to stop oscillations and find a new equilibrium position, though, you can turn up friction until the mass stops oscillating.

3. Note the new equilibrium position of spring 2 with a 100 g mass (as opposed to the un-stretched position of the spring with no mass). Be sure to measure the distance the spring has stretched with the ruler (which you can move around on the page). How does this position compare to the theoretically expected value?

4. Determine the spring constant k of the spring through any method you devise.

5. Once you have determined the spring constant, be sure you are using the 100 g mass, and pull it 10 cm away from equilibrium. Let the mass oscillate and use the stopwatch to carefully measure the period T of oscillation (determine your own method to determine it accurately).

6. With your determined values of k and T, make a plot in Excel of the theoretical Spring Potential Energy PE (as measured from the equilibrium position of the spring with the 100 g mass) vs. time from 0 to 1 second. Can you do it without help? If not, here are a series of hints. Hint 1. Hint 2. Hint 3.

7. Now we want to measure the velocity vs. time in order to plot Kinetic Energy KE vs. time. In lab, we would do this with a motion sensor, but, sadly, in a rebellious action from the virtual gremlins, the motion sensor was dragged from the simulation in order to protest unequal access to bathrooms for virtual vs. real beings. So you will need to compute kinetic energy and total energy (hint, compute total first, then kinetic).

8. Plot PE, KE, and total E on the same graph.

• Be sure to address questions and prompts in the previous section.
• Do the energy plots (KE, PE, E)  look like you expect? Do they have the expected relationships to each other? If not, you should probably figure out what is going wrong before you finish lab.
• If a non-conservative force such as friction or air resistance becomes important, the graph of total energy vs. time will change. What is the ideal shape of the total energy curve, and what is expected if friction is not negligible? Is friction negligible for your total energy E? Be sure to determine this quantitatively.

Post-Lab (at the discretion of the instructor)

1. Measure the mass of the largest, red mass.

2. Determine the acceleration due to gravity on Planet X.

Write-Up

1. If this is a formal lab (as indicated on the lab syllabus), you have been instructed as to whether this is an individual or group write-up, or an oral presentation. If it is a write-up, each person must submit the lab electronically as a word-processed document in Moodle before the next lab meeting. If it is a group write-up, you should all be submitting the same document. For written formal labs, remember to check the "write-up hints" page to be sure everything is included and check your write-up against the grading rubric.
2. If this is an informal lab, work on the results together in your groups, and be sure to have your complete informal lab in your lab notebook and checked by the instructor before you leave.
3. Remember to read the next lab and do the pre-lab before you come to lab next week! You may work on the pre-lab with others, but each person must submit her or his own work.

Department of Physics