Experiment #9 - Hooke's Law and Harmonic Motion
Copyright R. Mahoney 2014
Name: ____________
There are four purposes of this experiment. The first purpose is to show that Hooke's Law is
approximately true, at least within the elastic limit of the springs you will be testing. The
second purpose is to show that a spring's frequency of oscillation is a function of its bobbin
mass and its spring constant. The third purpose is to show that the above mentioned
frequency is not a function of the varying amplitudes of the oscillations. The fourth purpose is
to show how spring constants combine when hooked "in series".
1. Set up the spring apparatus as shown in class. Start with just the bare weight holder set at
a convenient "zero mark". As you add weights, make a note of the new position of the marker
relative to the scale. Use the mirrored surface of the scale and the weight holder's bottom
pointer to ensure that there is no parallax induced error in your readings. As you add weights,
do not overstretch the spring, or go past the largest reading on the scale. Write your data in
the columns following. When calculating the spring constant for each added weight, be sure to
multiply the mass added by g. For this experiment, you do not have to weigh the added
masses: just use the nominal values marked on the weights.
Mass added (kg)
Weight Added (N)
Change in pointer
position (m)
Spring Constant
(k1, N/m)
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What is the average of your five calculated spring constants (k1)?
Answer: ___________ N/m
2. Choose a mid-range weight suitable for smooth oscillation of itself when extended a small
amount from its rest position (this small amount is the initial amplitude). Test various
combinations of bobbin mass (which includes the weight holder) and amplitude, until you get
steady oscillations that are almost exclusively up and down (no side to side swaying) and a
period of oscillation of over 1 second.
a) What is the mass of the bobbin (m, include holder)? Answer: ___________ kg
b) What is the initial amplitude (A)? Answer: ___________ m
c) What is the total time for 50 oscillations? Answer: ___________ sec
d) What is the time, or period, for one oscillation (measured period, Texp)?
Answer: ___________ sec
e) What is the theoretical period for this spring-bobbin system (use the formula given in class,
use k1 for the spring constant, Ttheo)? Answer: ___________ sec
Calculate the percent error between the measured and theoretical periods for this springbobbin system. Answer: ___________ %
3. Repeat step 2, part c, but this time change the amplitude to a larger or smaller amount.
What is the total time for 50 bounces? Answer: __________ sec
Qualitatively, how different is this total time than the total time recorded in step 2c?
Answer: _________________________________________________________________
4. You will be supplied with a second spring, similar to the first. Use the method described in
step 1 to determine its spring constant. It does not matter if the second spring's spring
constant is similar to the first (it probably will be).
Mass added (kg)
Weight Added (N)
Change in pointer
position (m)
Spring Constant
(k1, N/m)
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What is the average of your five calculated spring constants (k2)?
Answer: ___________ N/m
5. Now hook the two springs together ("in series") and measure their "combined springs"
spring constant.
Mass added (kg)
Weight Added (N)
Change in pointer
position (m)
Spring Constant
(k1, N/m)
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What is the average of your five calculated spring constants (k)?
Answer: ___________ N/m
This is your experimental "combined springs" spring constant.
Now calculate the theoretical (true) value for the "combined springs" spring constant, using this
formula: k = (k1 x k2)/ (k1 + k2). Answer: ___________ N/m
Calculate the percent error between the measured and theoretical (true) values of the
"combined springs" spring constant. Answer: ___________ %