Revised 1.12.12

Name______Date______Per______

Simple Harmonic Motion Mini-Lab

20 points

Data Table (3 pts)

Run / Mass
/ y0
/ A / T
/ f
(g) / (cm) / (cm) / (s) / (Hz)
1 - 200g (small amplitude)
2 – 200g (large amplitude)
3 - 300g long (large or small)

Analysis (8 pts)

1.View the graphs of the last run on the screen. Compare the position vs. time and the velocity vs. time graphs. How are they the same?

How are they different?

2.Turn on the Examine mode by clicking the Examine button, . Move the mouse cursor back and forth across the graph to view the data values for the last run on the screen. Where is the mass when the velocity is zero?

Where is the mass when the velocity is greatest?

3.Does the frequency, f, appear to depend on the amplitude of the motion?

Do you have enough data to draw a firm conclusion?

4.Does the frequency, f, appear to depend on the mass used?

Did it change much in your tests? Explain.

READ THE FOLLOWING CAREFULLY

5.You can compare your experimental data to the sinusoidal function model using the Curve Fitting feature of Logger Pro. Try it with your 300-g data. The model equation in the introduction, which is similar to the one in many textbooks, gives the displacement from equilibrium. Your Motion Detector reports the distance from the detector. To compare the model to your data, add the equilibrium distance to the model; that is, use

where y0 represents the equilibrium distance.

To do a model:

First click on the graph that you want to model, then

Choose Analyze Curve Fit. Find the general equation as above. Note, it will be sine and not cosine. Then hit try fit. Note the values and how they relate to your values for y0, A, and f. The phase parameter  is called the phase constant and is used to adjust the y value reported by the model at t=0 so that it matches your data. Since data collection did not necessarily begin when the mass was at maximum distance from the detector,  is needed. Initially leave the value for  as is, but you may need to adjust it slightly so that two different graphs are able to be seen. (see picture below)

6. The optimum value for  will be between 0 and 2. By repeating the column modification process in step 5, find a value for  that makes the model come as close as possible to the data of your 300 g experiment. You may also want to adjust y0, A, and f to improve the fit. Write the equation from the data that you originally took above.

*write the equation in the exact same format as above. (except sine), calculate 2*pi*frequency – show this work on the print out for me to view. (2 pts)

(B represents 2*pi*frequency)

Print of both lab data(this sheet) and equation data

(note: you may need to make them slightly off to show contrast in a print)

Attach 300g print (or whatever mass you used for your first trial) (print 1 point + equation 2 points)

Repeat steps 5-6 with 200g either of the amplitudes

Attach 200 g print (or whatever mass you used for the next trial) (print 1 point + equation 2 points)

Sample print **including your variables for your equation