Appendix A: Example Report
NOTE: This is an example report that meets minimal requirements that would receive a passing grade. The
example lab that this report is written for is provided on canvas so you may compare along with the grading
rubric and the grade given for this write-up.
Reminder- The lab report is to be typed and then submitted electronically online through canvas. It is
recommended that you convert the document to a pdf before upload to prevent problems such as images not
being visible or data tables getting scrambled. The student is responsible to make sure that all graphs, tables,
images, symbols, equations, etc. are visible to the instructor and legible.
My name
Lab #20 Simple Harmonic Motion
Objectives
Today we are going to explore and learn about simple harmonic motion. We will look at how mass and
amplitude affect the period of oscillations of a mass and spring system. We will look at the speed of the mass
and the position of the mass throughout an oscillation.
Materials
I worked at lab Station #10 and my lab partners were Me, Myself and I. We will use a motion detector
connected to the computer via the interface and run the logger pro program. We will hang a spring off a hook
connected to a ring stand. The other end of the spring will be connected to a hanging mass that will be free to
move up and down.
Computer station #10
Partners: Me, Myself and I (5,4,1)
Verneir computer interface
Logger Pro
Motion Detector
Ring stand with hook clamp
Spring
Slotted weight set with hanger.
Meter stick/ruler
Index card
Tape
Preliminary Questions
1.
2.
Comparing my sketches to my partner’s I see that we agree on the basic shape but not on when crests occur,
or on the size or shape of the crests.
Lab partner’s graphs:
Procedure and Data
We attached the spring to a horizontal hook connected to the ring stand and then hung the mass hanger from
the spring at the other end. We placed the motion detector directly under it facing up and laying down.
We set the spring into motion and collected data.
Step 6.
Step 7. Comparing the actual graph to my prediction I see that I got the basic shape correct but am wrong in
the details of size, position and timing.
Steps 8-13: We calculated the equilibrium position of the hanging mass on the spring set an amplitude of 5
cm and recorded the motion. From the graph we calculated the period by taking the time at one crest and
subtracted off the time of a previous crest. Then we divided one by that number to calculate the frequency.
Then we did this all again for the same mass at 10 cm displacement and 60 g at 5 cm displacement. Data is
shown in table 1.
Data Table 1: Variables of SHM
y0
T
A
(g)
(m)
(cm)
(s)
(Hz)
1
50
.2161
5
.796
1.26
2
50
.2161
10
.81
1.23
3
60
.3241
5
1.114
.8977
Run
Mass
f
Analysis
1. The shapes of the graphs are fairly similar but the crests/trough of the two do not align. They are out of
phase.
2. The mass is at the top and bottom when the velocity is zero. The mass is at equilibrium when the velocity
is greatest.
3. The frequency, f, does not appear to depend on the amplitude of the motion, however we should do more
trials with a wider variety of amplitudes to know for sure.
4. Yes the frequency does appear to depend on the mass and there is a change between the two tests.
5.
y=A*sin(Bt +C) + D matches our y = A sin (2πft + φ ) + y 0 equation where y0 represents the equilibrium
distance and is D, the phase is C, B is 2pi frequency, and amplitude is A in both equations.
Our best fit is y=.03sin(14(3.14)T+3.9)+2.0
6. It fits ok but not exactly. It gets more off with time.
7. It would increase the amplitude.
8. The peaks would get much closer together.
Extension:
Add Dampening:
We taped a piece of paper to the bottom of
the hanger to increase the influence of air
resistance. The amplitude of oscillations
lessens with time and then stops all together.
There does not seem to be an effect on period
or frequency.
Conclusion
In conclusion we were able to show how amplitude and mass affect the frequency and period of SHM by
adjusting those parameters to see how the other variables changed. From our data we have concluded that
amplitude has no effect on frequency but mass does. As mass increases, frequency decreases. We were able
to compare our graph to the equation for SHM by fitting a curve to our best data collection. It fit well but
gets off with time, this error is likely do to friction in the system that we are not accounting for with the fit
and the spring had a tendency to start to swing like a pendulum. From our fit we were able to see how
frequency and amplitude are used to mathematically express SHM. From our graphs of p vs t and v vs t we
concluded that the mass has its greatest velocity while traveling through the equilibrium position and the
velocity will be briefly zero the instant the mass is at its highest and lowest points where the amplitude of
oscillation is maximum.