Worcester Polytechnic Institute
PH 1140
Experiment #2: Mass-Spring Oscillator
ReadMeFirst, Experiment #2, Part 1, Measurement of Spring Constants.
(Once read, please resize to fit in the bottom couple of inches of the screen so that this
ReadMeFirst document can be easily referenced anytime during Part 1.)
In this first part of the experiment, you will be measuring the spring constant of one individual
spring plus a somewhat complicated arrangement of four similar springs.
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At your station there is a tall ring stand with a Vernier Dual-Range Force Sensor attached
to a cross-bar located up near the top. Make sure that the Force Sensor switch is set in the
±10 N position. There is also a Vernier Motion Sensor looking straight up at the Force
Sensor from its position on the lab bench directly underneath the Force Sensor. Also at
your station you should find four springs (one painted red, and the other three unpainted), a
50-g mass hanger, and several slotted masses (1 50-g and 9 100-g).
Open the SpringConstant Logger Pro template, also contained in this Part 1 Folder. With
the single red spring plus mass hanger (NO slotted masses) hanging from the Force Sensor,
click on the “Zero” button up on the main tool bar (a bit right of center). When the Zero
Sensor Calibration box opens, click OK (in order to zero both the Force and Motion
Sensors).
Add the 50 g slotted mass to the mass hanger so that there is a total of 100 g now hanging
from the Force Sensor. (You should also note that the coils of the spring are now separated
from one another because of the application of this additional mass.)
IMPORTANT NOTE!!! Always handle the slotted masses so as NOT to drop them on the
Motion Sensor below. Hold the slotted masses firmly until they are securely on the mass
hanger, and if hooking or unhooking the hanger from the spring while slotted masses are on
the hanger, be sure to cup your hand around the masses as well as the hanger during that
hooking or unhooking so as to prevent the slotted mass from falling off the hanger.
Damp out any up/down or side to side motion of the mass hanger. When it is quite
stationary, click the Collect button (which then becomes a Stop button), and also click the
Keep button. Then add a 100-g mass to the hanger, damp out any hanger motion, click
Keep, and continue adding mass 100 grams at a time until you have reached a total mass of
600 grams. Again click Keep for this last mass value, and then click Stop to end the data
collection.
You can determine the spring constant of the active spring by a least-squares fit of your
collected data! Click on the “R=” button on the tool bar. Note that the six datum points
you have collected sit on a straight line with very little deviation from that line. That is
testament to the LINEARITY of the spring! Right-click on the data box and, within the
Linear Fit Options, select 5 under Displayed Precision and check the Show Uncertainty
box. After you close that box, you will find the slope, complete with uncertainty, both
presented to 5 figures. It is now up to you to write down this red-spring spring constant in
proper form (uncertainty rounded to one non-zero digit unless that non-zero lead digit is 1,
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in which case you round to two digits; then round the spring constant to the same decimal
place as the right-most digit of the uncertainty) on a sheet of scratch paper for future
reference.
Repeat all steps in this procedure for the other, somewhat complicated arrangement that
your lab instructor will describe for you (a series, parallel arrangement of 4 similar springs,
one of which will be the red spring), BUT with the following variation. Use the same
Logger Pro template as before, but this time “Zero” the two sensors with the mass hanger
PLUS 50 g hanging from the spring arrangement. Then after zeroing, begin measuring
force versus extension with another 100-g mass added for a total hanging mass of 200 g.
Then obtain four more datum points by adding masses in 200-g increments up to a total of
1000 g. Save each datum point along the way, and determine the spring constant of this
somewhat complicated arrangement in the same manner as before.
Write down the spring constant for this new arrangement on your scratch paper in the usual
industry-standard way. Note that because all four springs have approximately the same
spring constant, the spring constant for the series-parallel arrangement is about the same as
for the red spring by itself. (In Experiment #1, you learned the rule for determining the
spring constant of two springs in series – the reciprocal of the series spring constant is
simply the sum of the reciprocals of the individual spring constants. Turns out that the net
spring constant of springs in PARALLEL is simply the SUM of the spring constants for the
two spring arrangements in parallel.)
This ends Part 1. Close this folder and open the Part 2 folder.