Lab
Oscillating Springs
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Purpose
The purpose of this lab is to investigate the behavior of a vibrating spring. Initially we will use a LabPro to collect frequency data on 10 different mass combinations. Then we will use linear analysis to determine the spring's force constant, k. Finally you will be asked to determine the energy in the oscillating system as well as instantaneous velocities and accelerations.
Equipment
spring
slotted masses
mass hanger
support stand
LabPro
Data Collection
Complete ten trials ranging from 150 grams to 950 grams. There is no need to displace the pan by more than 1 to 2-cms. Collect data for 15 complete vibrations. I would suggest that each trial be done two times, and then record the average duration as the value on your EXCEL graph.
Before dismantling your equipment, investigate whether increasing the amplitude of oscillation will make a difference in the period of a 950 gram mass. [ALERT: do NOT under any circumstances use an amplitude greater than 5 cm]
low amplitude
trial number 1
trial number 2
mass
duration
(sec)
# vibrations
frequency
(hz)
period
(sec)
T
^{2}
(sec
^{2}
)
duration
(sec)
# vibrations
frequency
(hz)
period
(sec)
T
^{2}
(sec
^{2}
)
0.150 kg
0.250 kg
0.350 kg
0.450 kg
0.550 kg
0.650 kg
0.750 kg
0.850 kg
0.950 kg
higher amplitude
trial number 1
trial number 2
mass
duration
(sec)
# vibrations
frequency
(hz)
period
(sec)
T
^{2}
(sec
^{2}
)
duration
(sec)
# vibrations
frequency
(hz)
period
(sec)
T
^{2}
(sec
^{2}
)
0.950 kg
After all of your data has been collected, open the EXCEL file for
SHM
and enter your data for Mass, T, and T
^{2}
. Save your graph with the filename:
LastnameLastnameSHM.xls
and print one copy.
Conclusions
What was the name of your file?
What is the original unstretched length of your spring's coils?
1. Once you print your graph, use the form y = mx + b to rewrite the equation for your regression line using T
^{2}
and M as your variables as well as your data's exact slope and y-intercept.
What is the equation (with correct variables) of your line?
2. On your printout, solve for your spring's elasticity constant, k, by modifying the formula T = 2 π √(m/k) to parallel the format of your regression line's equation and solve for k. [HINT: you need to show the derivation to prove that the slope of the line equals the expression 4π
^{2}
/k ]. Make sure that k is expressed with the correct units.
What is your value for k?
3. Why were you not asked to analyze a graph of T vs M?
4. Did the period ____ as the total mass was increased?
decrease
remain the same
increase
5. Would the period ____ if the spring constant was increased?
decrease
remain the same
increase
6. How was the frequency affected in your final trial when the amplitude of the spring's oscilation increased?
SHM Equations
For the purpose of the next section, you will use the spring constant from your EXCEL graph.
7a. Based on your spring constant, how far would the coils of your spring stretch when a 650-gram mass is placed on it? This position will henceforth be referred to as the equilibrium position.
7b. How much elastic potential energy would be stored in the coils of your spring while it is at its equilibrium position?
8. Assume that you release your spring with its 650-gram mass by intially compressing it 2.0 cm. How much total energy did you supply to the system prior to its release?
9. From your data table, what was the average frequency (in hz) when a 650-gram mass was attached to the spring?
10a. Which graph shown below would represent your spring's initial behavior?
10b. State the position equation for your spring's oscillations.
11. After release, when, in seconds, did your mass first pass through its equilibrium position?
12. What was the velocity of your mass, in m/sec, as it passed through its equilibrium position?
13. What was the velocity of your mass as it passed through the lowest point in its oscillation?
14. What was the magnitude of your mass' maximum acceleration while it was oscillating?
15. What was its instantaneous acceleration at exactly 15 seconds when each trial concluded?
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Worksheet:
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Introduction to Springs
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Kepler's Laws: Worksheet #2
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Pendulum Lab Review
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Practice: SHM Equations
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Practice: Uniform Circular Motion
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SHM Properties
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