Optics and Modern Physics Lab
Fall 2015
Dr. Pogo
Week 0: Error Propagation and Using Excel’s “Solver”
Name:_____________________________________
Installing/activating Solver in MS Excel 2013:
1. From any open document, click the “File Tab”.
2. Go to “Options” at the bottom left.
3. Choose “Add-Ins” at the bottom.
4. Click the GO button at the bottom center.
5. Select the “Solver” add in (and any others you want).
6. To use Solver after it has been activated, choose the “Data”
menu; solver is now way over on the right side.
Assignment (also, make sure you see the other side, too!)
1. Enter this data set.
2. Plot it. Have labels as appropriate. Note that as always, measured data
points should have dots/markers but NO connecting lines.
3. Use Solver to find the equation of the best fit line for this data: x = b + mt.
Record all answers in the appropriate box below using three sig figs.
4. Then find the best fit parabola: x = a0 + a1t + a2t2.
5. Then find the best fit exponential: x = C1 + Aekt (force C1 > 0).
6. Then find the best fit sine wave: x = C2 +Bsin(ωt). For this case, you
probably need reasonably good starting guesses (all parameters positive).
7. Report your results below for the various constants you’ve found. Use 3
sig-figs for each. Hint: most of these constants are numbers with units. Excel
only tells you the number part, but you must tell me both.
b=
8. All of these fits were found using the method of least squares.
Which of these four fitting methods gave the “best” results? How do
m=
you know?
9. Add only the best of these fits to your plot and reformat it to make
error2 =
sure it uses only the top 3rd of a sheet of paper. Don’t print it yet.
a0 =
C1 =
C2 =
a1 =
A=
B=
a2 =
k=
ω=
error2 =
error2 =
error2 =
Which fit is best?
How do you know?
.
time
(ms)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
position
(mm)
130
140
149
158
167
175
183
191
198
205
209
215
219
222
225
226
226
227
227
227
228
Optics and Modern Physics Lab
Fall 2015
Dr. Pogo
10. Consider the following plots. In each case, circle the features that should be improved, and annotate
each of your circles with a number corresponding to the “Rookie mistake” that it represents.
11. Choose any two of the first 4 plots shown here, and then replot them in a more appropriate way on
the same sheet as before (see above steps 2 and 9). I don’t want to see data, just plots. You may have to
adjust margins, etc. as well as the individual plots. You can find the original data online at:
http://www.geneseo.edu/~pogo/OpticsLab/PlottingRawData.xls
12. Staple your one extra sheet having 3 plots on it to this worksheet, and turn it in next week. Do not
ask your instructor for a staple.
0.0000304
3
0.00003035
2.5
y = 1E-05x + 3E-05
0.0000303
0.00003025
Series1
1.5
Amps
2
0.0000302
0.00003015
Current (Amps)
0.0000301
1
Linear (Current (Amps))
0.00003005
0.5
0.00003
0.00002995
0
0
0.0
1.0
2.0
3.0
4.0
0.01
5.0
P/T^4
0.02
0.03
0.04
Meters
1.2
4.6E-14
1
4.6E-14
0.8
4.6E-14
0.6
4.6E-14
0.4
4.6E-14
0.2
4.5E-14
0
P/T^4
Series1
Series2
Series3
Series4
Series5
Series6
0
4.5E-14
4.5E-14
800.0000 1133.000 1466.000 1799.000 2132.000 2465.000 2798.000 3131.000
0
00
00
00
00
00
00
00
T
0.5
1
1.5
2
2.5
3