Lab 1: Period and frequency



Lab 4: Rubber band oscillatorObjectivesBy the end of this lab you should be able to:Test the model for a mass-spring system using measurements of frequencyWhat to submit:Summary report to D2L under Assignments/Lab04Excel spreadsheet showing graph and analysisMaterials: You may take your oscillation data from the lab video, or run your own experimentComputer with internet connectionStop watchExcel (available for free on Office 365 link on D2L) To use lab video data: experiments start around minute 12 To set up your own experiment:10 rubber bands of the same size, chained togetherA mass (something convenient, keys on a keyring, maybe?)Definitions:Period: time for one complete cycle of vibration (symbol T)Frequency: the number of vibrations per second (symbol f=1/T)Simple harmonic oscillator (SHO): A vibrating system where the restoring force is proportional to the displacement.BackgroundIn science, we are often dealing with incomplete information. To fill in the gaps, we construct a model, that has clearly outlined assumptions. From this, we make predictions, and if those predictions are verified by experiment, we say this validates all the assumptions and reasoning of the model. By checking and cross checking we build up confidence in these assumptions. Therefore, checking the model and experiment are essential aspects of science, and both are equally important.We learned that the simple harmonic oscillator frequency model for a mass-spring system depends on the stiffness of the spring and the amount of mass on the end of the spring. (The spring itself is considered to have zero mass.) The frequency model is given by . ……………………………….(1)This model is important in musical acoustics because it gives us an idea why vibration frequencies take the values they do. It depends on the stiffness of the vibrating material and its mass. This must be modified in complex real systems, but the overall idea is similar.1) Make a prediction Which graph best shows how the frequency model depends on stiffness? Indicate a, b, or c. Include an Excel graph to support your answer. To determine this, you will make a plot. Set all quantities not changing (everything except stiffness) to 1, and make a plot of the model formula using Excel. See lab video for hints. Note that the example in the video is different from what you are being asked here. You have free access to download Excel through Office 365. See lab video.We will test this model by a simple experiment using rubber bands. We start with 10 identical rubber bands with the same size and stiffness. We then create a chain. If you were to jump off your roof onto a pillow, would you want n=1 or n=10 pillows? You want n as large as possible, because when you chain elastic things together, the stiffness goes down as the number goes up! If you don’t believe this, try this with a few rubber bands. Many people are quite surprised.By using n=1, 2, 3, etc. rubber bands in the chain, we can change the stiffness. Assuming identical rubber bands in series, and taking the stiffness of one rubber band as 1 unit, the stiffness of a chain of n rubber bands :If you would like to make your own rubber band chain and do your own experiments, see the lab video for how to make a rubber band chain. Otherwise, you can take your measurements from the lab video.To take data, we hang a mass on the end of the rubber band chain, and let the system vibrate. We will take data for n=1, 2, 3, 4, 5, 10 rubber bands, and measure the period of vibration. We will perform three trials for each. What to do:When the mass is released, start the timer, and mentally count 0. Watch the oscillation and when it returns to its starting point that is a mental count of 1 cycle. Continue this process. Stop the timer at a count of 5 cycles and record this time. The period is this number divided by 5.What NOT to do:Some people measure the time until the vibration movements are no longer visible. This is NOT a correct measurement of period.After you have collected three trials for the period T using n=1, 2, 3, 4, 5, and10 rubber bands, use Excel to calculate the frequency of each trial. See lab video.Then take the average and uncertainty of the frequency. See lab video. We will use the Excel commands AVERAGE (for average) and STDEV (for uncertainty). Plot both the data and the model on the same graph, with error bars. See the lab video for details.To compare the model and the data, multiply every value of the column by the f average for the case of 1 rubber band. See lab video. You should see the graph update automatically. This adjusts the model to include the actual stiffness value of one rubber band and the mass used in the experiment.Then answer the lab summary questions. Submit to D2L under Assignments:Your lab summary template answersExcel spreadsheet Lab04 summary template for submission to D2L (10 pts) Make a prediction Which graph best shows how the frequency model depends on stiffness? Indicate a, b, or c. Include an Excel graph to support your answer.(10 pts) a) Describe how you took your data. If you did your own experiment, describe it. If you used the data in the video, discuss how you did your measurements. B) Cut and paste the final Excel graph comparing your model and data here. Be sure that you: include axis labels and units, a title, and include Y error bars on your data. (10 pts) Recall that error bars indicate the range of values obtained under the same experimental conditions, and reflect our ability to reliably measure something. Think back to your measurements of the period, and which measurements were more challenging. Now look at your graph, and where the error bars are largest. Are these consistent? Discuss.(10 pts) Discuss whether the model is generally in agreement with the data. Are the values within 3 error bars (is the significance ratio less than 3) for all data points? (10 pts) Recall that when the model and the data are in disagreement, all assumptions are called into question. The graph compares the behavior of the rubber band chain relative to the first band in the chain. One assumption we applied was that the rubber band chain consisted of identical bands of equal stiffness. Suppose the n=10 data on your graph was significantly below the model graph. If the identical rubber band assumption is wrong, develop a scenario that would explain this observation. ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download