Lab
Water Springs
Printer Friendly Version
This lab was designed in 1995 for "A Day in the Life of a Student in the 21st Century" - a teleconference with the US House committees on science, economics, and educational opportunities.
Purpose
The
purpose
of this lab is to produce an oscillation that has a varying amplitude yet constant period. As the mass is dragged through the water, the amplitude of the spring's oscillation decreases as the energy stored in the spring is transferred to the water. This is an example of a
damped oscillation
in which the amplitude is experiencing an exponential decay.
Lambda, λ
, represents the decay function of this damped oscillation. During our analysis, we will first graph the spring's
amplitude vs time
and then examine a second graph of the
natural logarithm of its amplitude vs time
. The slope of LN(y) vs t will be negative lambda, -λ. Using this slope we will determine the half-life of the spring's decay and verify its value with the data collected from the LabPro distance probe today.
A typical graph of this type of oscillation would look like the following sample.
Equipment
LabPro motion detector
plastic ½ gallon milk jug with water
spring
700 grams of slotted masses
one mass hanger (50 grams)
white index card
tape
Procedure (set-up):
Under the Start Menu go to Programs, Math, Logger Pro 3.1 to launch the program. Logger Pro should automatically set up the graphs according to the connected sensor. With the Motion Detector properly connected, the program should display graphs of position vs time and velocity vs time. Press Collect to test your connections. Make sure that you are collecting data to at least 3 decimal places.
A second member should verify that the probe can see the white book card attached to the bottom of the spring - just above the top of the milk jug. Note that only slight adjustments should be necessary! When the spring is gently oscillated, the card should not rub against the container or twist violently. Note that the masses (750 grams total) MUST remain completely submerged in the water during each trial and NO water should be splashed out of the container. Verify that the probe is seeing the card by moving the masses carefully up and down -- Do NOT use large amplitudes! 5-6 cm is MORE THAN ENOUGH! When everything is working, you are ready to start collecting data.
Procedure (data collection):
Since the spring needs a few seconds to stabilize, the person releasing the spring should tell the Logger Pro operator when to start the probe. Try to release your spring with a small steady amplitude and a minimal amount of rotation (twisting). Watch your graphs. The oscillations should minimally have either a constant set of smooth crests OR smooth troughs -- it is not absolutely necessary to have perfect oscillations in both places. When you have a good trial, highlight a "good section" of your position vs time graph. The data selected will be highlighted in the accompanying data table. Copy and paste your data into an EXCEL spreadsheet. Rename the sheet Data I.
Finally, carefully rerun the experiment and obtain a second trial. Save this one on a sheet called Data II. Run your trials as accurately AND quickly as possible, remember that at least one other group needs to use your lab station before the period is over.
When you are finished with both trials, leave the spring, card & masses suspended in the water jug. Please wipe up any water that may have been dripped onto the table. Exit from Logger Pro so that the next group can begin.
Analysis (regression theory):
Input your best data into the following EXCEL spreadsheet,
WaterSpringAnalysis.xls
. From there, we will determine the half-life of your damped oscillation.
Conclusions
What is the slope of your line of best fit?
Using this slope, what is the half life, T
_{½}
, of your spring's oscillation?
In EXCEL, open your spreadsheet and fill out the following data table by scrolling down your data table in column A until you find the time for the fifth maximum in column F. Note the corresponding value of its amplitude in column C and record both in your chart. Then scroll down to the time closest to the passage of one half-life. Record that time from column A and its corresponding value for the amplitude in column C. Continue this procedure until a total of five values have been listed. Then use the definition of half-life to complete the column entitled ideal amplitude value based on the value for the amplitude of your initial time.
actual
ideal
description
time
amplitude
amplitude
(col A)
(col C)
(half-life)
initial time
initial + 1 T
_{½}
initial + 2 T
_{½}
initial + 3 T
_{½}
initial + 4 T
_{½}
Did the decay in the spring's amplitude, as reflected by the changes in its values in the previous table, behave according to the definition of half-life?
yes
no
Support your answer by using you data analytically to calculate a percent error for your closest example.
Related Documents
Lab:
Labs -
A Physical Pendulum, The Parallel Axis Theorem and A Bit of Calculus
Labs -
Calculation of "g" Using Two Types of Pendulums
Labs -
Conical Pendulums
Labs -
Conical Pendulums
Labs -
Conservation of Energy and Vertical Circles
Labs -
Introductory Simple Pendulums
Labs -
Kepler's 1st and 2nd Laws
Labs -
Loop-the-Loop
Labs -
Moment of Inertia of a Bicycle Wheel
Labs -
Oscillating Springs
Labs -
Roller Coaster, Projectile Motion, and Energy
Labs -
Sand Springs
Labs -
Simple Pendulums: Class Data
Labs -
Simple Pendulums: LabPro Data
Labs -
Video LAB: A Gravitron
Labs -
Video LAB: Circular Motion
Labs -
Video LAB: Looping Rollercoaster
Resource Lesson:
RL -
A Derivation of the Formulas for Centripetal Acceleration
RL -
Centripetal Acceleration and Angular Motion
RL -
Conservation of Energy and Springs
RL -
Derivation of Bohr's Model for the Hydrogen Spectrum
RL -
Derivation: Period of a Simple Pendulum
RL -
Energy Conservation in Simple Pendulums
RL -
Gravitational Energy Wells
RL -
Kepler's Laws
RL -
LC Circuit
RL -
Magnetic Forces on Particles (Part II)
RL -
Period of a Pendulum
RL -
Rotational Kinematics
RL -
SHM Equations
RL -
Simple Harmonic Motion
RL -
Springs and Blocks
RL -
Symmetries in Physics
RL -
Tension Cases: Four Special Situations
RL -
The Law of Universal Gravitation
RL -
Thin Rods: Moment of Inertia
RL -
Uniform Circular Motion: Centripetal Forces
RL -
Universal Gravitation and Satellites
RL -
Vertical Circles and Non-Uniform Circular Motion
Review:
REV -
Review: Circular Motion and Universal Gravitation
Worksheet:
APP -
Big Al
APP -
Ring Around the Collar
APP -
The Satellite
APP -
The Spring Phling
APP -
Timex
CP -
Centripetal Acceleration
CP -
Centripetal Force
CP -
Satellites: Circular and Elliptical
NT -
Circular Orbits
NT -
Pendulum
NT -
Rotating Disk
NT -
Spiral Tube
WS -
Basic Practice with Springs
WS -
Inertial Mass Lab Review Questions
WS -
Introduction to Springs
WS -
Kepler's Laws: Worksheet #1
WS -
Kepler's Laws: Worksheet #2
WS -
More Practice with SHM Equations
WS -
Pendulum Lab Review
WS -
Pendulum Lab Review
WS -
Practice: SHM Equations
WS -
Practice: Uniform Circular Motion
WS -
Practice: Vertical Circular Motion
WS -
SHM Properties
WS -
Static Springs: The Basics
WS -
Universal Gravitation and Satellites
WS -
Vertical Circular Motion #1
TB -
Centripetal Acceleration
TB -
Centripetal Force
PhysicsLAB
Copyright © 1997-2019
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton