Use data logger to investigate Simple Harmonic Motion - Mass on a
Spring
Apparatus
Pasco Science Workshop 750 Interface, stand and clamp (for holding the spring), force sensor,
masses and mass hanger, motion sensor, meter-rule, spring, paper card.
Objective
The purpose of this laboratory activity is to investigate the motion of a mass oscillating on a
spring.
Previewing Questions
1.
What is the motion of a mass oscillating on a spring? What other motions can you think
of that are similar?
2.
A 0.2 kg mass is attached to the lower end of a vertical spring of force constant 5.0 N
-1
m . What is the natural frequency of the mass-spring oscillator?
Experiment 1: Determining the Spring Constant
Part A: Computer Setup
1.
Connect the data-logger interface to the computer, turn on the interface, and turn on the
computer.
2.
Connect the force sensor’s DIN plug into Analog Channel A of the interface.
Figure 1
3.
3.
4.
Run DataStudio. Associate the force sensor icon with the interface as shown in figure
1.
To enter the stretch of the spring manually:
Click the “Option” button (
). In the Sampling Options window, check the
“Keep samples on button or menu item command” and “Keep manually entered data
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values with samples”. The Data Properties Window will pop-up. Enter stretch in the
“Name” field. In Y variable tag, enter the following fields: Variable Name = x, Unit = m,
Accuracy = 0.001, Precision = 3 and Variable type=other. Click OK to close the dialog
window.
Figure 2
5.
Drag the force item from the Data Panel to the Table Display Panel. Table 1 will be
displayed. Uncheck the clock button (
) to disable the timing function. Drag also the
stretch item from Data Panel to table 1 in Display Panel. The result will be shown as in
Figure 2.
Force
sensor
Spring
Equil. position
x
Figure 3
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M
Metre rule
Part B: Equipment Setup
1.
Mount the force sensor vertically so its hook end is down.
2.
Suspend the spring from the force sensor’s hook so that it hangs vertically.
3.
Use the metre-rule to measure the position of the bottom end of the spring (without any
mass added to the spring). Record this measurement as the spring’s equilibrium position.
Part C: Data Recording
1.
Press the “tare” button on the side of the force sensor to zero the force sensor.
2.
With table 1 open, click the “Start” button to begin data recording. Click “ “ to record
the force. In the stretch field, enter 0 (since the spring is not stretched yet)
3.
Add 40 grams of mass to the end of the spring (be sure to include the mass of the hanger).
4.
Click “ “ to record the force. Measure the new position of the end of the spring. Record
the difference between the new position and the equilibrium position as “Stretch” (in
meters).
5.
Continue to add mass in 20 gram increments until you have added 120 grams. Each time
record the force and stretch.
6.
Double-click the Graph in Display Panel with show the result.
Part D: Analyzing the Data
1.
2.
3.
Click the “Fix” button (
). Select “Linear Fit”. Record the slope of the line.
The slope of the best fit line of Force versus Stretch is the spring constant “k”.
Record the value of spring constant “k”
Experiment 2: Recording the oscillatory motion of the mass-spring system
Part A: Equipment Setup and Sensor Calibration
1.
Unplug the force sensor’s DIN plug from the Science Workshop interface.
2.
Connect the motion sensor’s plugs into Digital Channels 1 and 2 of the interface. Plug
the yellow-banded (pulse) plug into Digital Channel 1 and the second plug (echo) into
Digital Channel 2.
3.
Run DataStudio . Associate the motion sensor icon.
4.
Set the properties of the motion sensor:
Double-click the sensor icon to display the Sensor Properties dialog window. Click the
Measurement tab. Select Position and Velocity. Click the Motion Sensor Tab. Set
the Trigger Rate (sampling rate) to 100 Hz. Click OK to close the dialog window.
5.
Open the Graph display window to show position-time, velocity-time and
acceleration-time graphs:
Drag the position item from Data pane l to the Graph display icon of the Display
panel. A blank position-time graph will be shown. Drag the velocity item from the
Data Pane l to the Graph display window. When the dotted line rectangle occupies
the entire window, release the mouse button. Two blank graphs will appear with
one above the other. Click the “Align Matching x-scale” button (
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) so that the
time axes are using the same scale.
Part B: Data recording
Spring
M
Minimum distance = 30
cm at closest approach
To interface
Motion sensor
Figure 2
1. Using a stand and clamp, suspend the spring so that it can move freely up-and-down. Hang a
mass of 100 gram to the end of the spring.
2. Place the motion sensor at about 0.20 m directly beneath the mass hanger. The ultrasonic
beam should be set at “narrow” mode.
3. Pull the mass down about 20 cm and then release it. Let it oscillate a few times.
4. Click the “Start” button to begin recording data.
5. The plots of the position and velocity of the oscillating mass will appear in the Graph display.
Continue recording for about 10 seconds.
6. Click "STOP" button to end data recording.
7. “Run #1” will appear in the Data list in the Experiment Setup window. Repeat the experiment
if the result is not satisfactory.
Data Analysis
1.
Click the “Scale to fix” button to rescale the Graph display.
2.
Click the “Smart Cursor” button. The cursor changes to a cross -hair when you move it
into the display area of the graph. The X- and Y-coordinates of the cursor’s position are
shown next to the horizontal and vertical axes.
3.
Use the Smart Cursor to find the average period of oscillation of the mass. Move the
cursor/cross-hair to the first peak in the plot of position versus time and read the value of
time (shown below the horizontal axis). Record the value of time in the Data Table.
4.
Move the Smart Cursor to each consecutive peak in the plot and record the value of time.
5.
Find the period of each oscillation by calculating the difference between the time for each
successive peak. Find the average of the periods. Record your result.
m
.
k
Determine the phase relationship between the three graphs. The following procedures
may help to study the phase relationship in conventional way:
Compare your result with the theoretical value using T = 2π
6.
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Click the down arrow of the Settings (
7.
). Select Multiple Y-scale. Zoom in
the graph to display at least two cycles. Use the Smart tool (
) to determine
the time delay between graphs.
Save the data file using file name “shm.ds” and print hardcopies of the three graphs
Questions
1.
Account for the sources of error in this experiment.
2.
How does your calculated value for the period of oscillation compare to the measured
value for the period of oscillation? Find the percent difference between your calculated
value and the measured value.
Reminder: percent difference =
3.
4.
calculated − measured
calculated
× 100%
When the position of the mass is farthest from the equilibrium position, what is the
velocity of the mass? (Hint: Move the Smart Cursor to a peak on the position plot, hold
down the Shift key, and move the Smart Cursor onto the velocity plot. The velocity will
be given next to the vertical axis.)
When the absolute value of the velocity of the mass is greatest, where is the mass relative
to the equilibrium position?
Experiment 3: Studying the damped oscillation of the mass-spring system
Data recording
1.
Open the Graph display window to show position-time graph only.
2.
Fix a large card to the bottom of the hanger to increase the damping.
3.
Repeat experiment 2.
Data Analysis
1.
The motion is called damped oscillation Describe the motion.
2.
Measure the amplitudes Ao, A 1, A2, A3, etc. of the oscillations and enter the results in
the table.
3
Plot a graph of amplitude vs time on the graph paper.
4
Save the data file using file name “Damped oscillation.ds” and print the hardcopy of the
graph.
Questions
1. What does the card do to the oscillation?
2. From the amplitude-time graph, show that the amplitude decreases exponentially with time.
3. Do you find that the period of a damped motion is slightly larger than that of the undamped
one? If yes, explain why.
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