L20-3.  Simple Harmonic Motion of a Vertical Spring, Part 3

Enter your alias.

 

Use the same spring as you used in the previous two parts.  Enter your spring constant for reference.

N/m

Part 3a. Position vs. time of the oscillating mass

Complete the L20-3 Prelab questions on WebAssign before continuing below.

For the measurements below, use the sonic ranger and Logger Pro.  Also, use 0.250 kg on the spring as in the last part.  Set up the software as follows.

  1. Go to Experiment Menu, Data Collection, Collection tab, and change the sampling speed to 30 samples/sec. Also, set the experiment length to 5 seconds. Click OK
  2. Go to Insert Menu, Graph, and click on the label of the y-axis of the graph that appears. Select Distance Only. Click OK. You should have a position vs. time graph now. Click on the y-axis itself, go to axes options, and press manual scaling. Enter 0.4 m as the min. value, and 0.8m as the max.
  3. Set the spring into oscillation. Click Collect to start data collection. You should obtain a smooth, sinusoidal graph. There may be stray points toward the end of the time interval if the spring starts to sway from side to side. Save your file with the name L20-3a-alias.cmbl.
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  4. Upload your Logger Pro file to Moodle.

The goal is to determine the equation of the function that you just saved. That means you'll need to determine the equilibrium position, the amplitude, the period, and the phase shift. You've already practiced these things in the prelab, so you shouldn't need to spend much time discussing them with your partner except possibly for how you'll determine the phase shift. One method you may not use at this point is a curve fit. That would sidestep the learning that this lab is intended to provide. Describe below the methods that you use to determine the indicated things.

How will you determine the equilibrium position?

How will you determine the amplitude?

How will you determine the period? (Use the position vs. time graph rather than the value that you determined in Part 2 of the lab.)

How did you determine the phase shift?

Now carry out your methods. Give final values below in SI units but don't enter the units in the text boxes.

Give the value that you determined for the equilibrium position.

m

Give the value that you determined for the amplitude.

m

Give the value that you determined for the period.

s

Give the value that you determined for the phase shift in radians.

rad

Now write the equation of the position vs. time function. Use the values (with units this time) that you determined for equilibrium position, amplitude, period, and phase shift. You may use a sine or cosine function. Hopefully, you know why either function is acceptable.

Perform the following checks on your equation.  Substitute the time coordinate for one of the data points into your equation to see if you get the correct position. Each partner should select a different time coordinate, calculate the corresponding position coordinate, and compare to the actual time coordinate read from the graph.

Partner Time coor-
dinate (s)		 Calculated Position
Coordinate (m)		 Position Coordinate
Read from Graph (m)  		% Difference

Part 3b. Position, velocity, acceleration, and force relationships

In this part of the lab, you’ll measure the displacement, velocity, and acceleration of the spring with the sonic ranger at the same time that you measure force with the force probe. 

  1. Open the software in the same way as Parts I and II:  In the Logger Pro software, select the File menu, Open, and choose the Experiments directory, then Probes & Sensors, Motion Detector, MOT&DFS.  Press Open.

  2. Go to Experiment, Data Collection, Collection tab, and set the experiment length to 2 seconds and the sampling speed to 30 samples/sec.  Press OK.

  3. Calibration:  You first need to calibrate the probe to measure force in newtons. To do so, use the following procedure:

  1. Remove all weights, except the spring.

  2.  Go to Experiment Menu, Calibrate, and select the CH1 device (Dual Range Force).

  3. If the software presents an error reading, "The default calibrations folder could not be found,” or "The folder does not contain the correct calibrations,” then press OK to these errors. Click Cancel on the calibrations screen, and select File Menu à Preferences. On the "Default Folder" feild, press the Browse/Modify button next it. Select the C:\Program Files\Vernier Software\Logger Pro 2.0\Experiments\ folder. Press OK. This will remedy the error message. Select Experiment à Calibrate again.

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  4. Press Calibrate Now.

  5. The probe sends an electric signal in the form of a voltage to the interface/computer.  This voltage will be displayed now.  Wait for the voltage reading by "Channel 1" to stabilize, and type "0" (zero) into the Value 1 box,  and press Keep.  You just informed the interface/computer that this voltage corresponds to a reading of 0 Newtons on the force probe.

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  6. Now hang a total mass of 0.350 kg on the spring.

  7. When the voltage reading stabilizes again, enter the corresponding force in Newtons to 3 significant figures in the Value 2 box and press Keep (you have to figure out this force value).  You just informed the interface/computer that this voltage corresponds to a reading of newtons on the force probe.

  8. Now the probe/interface/computer combination has all of the information needed to convert voltages to the correct corresponding force values.

  1. The software probably opened with a block of 3 graphs ---distance, acceleration, and force-vs-time.  Insert a fourth graph to plot velocity vs. time. Select Page, Auto Arrange to display all windows without overlap.

    2.

  2. You should already have 0.350 kg total mass on the spring.  Set the mass into oscillation and collect data.

  3. You should get a smooth curve for the position and force graphs, but the velocity and acceleration graphs may show some scatter in the points.  (This has to do with the method used to calculate velocity and acceleration from the position data.) Select View, then Autoscale if the curves are not showing on any of the graphs. Then collect data as before.

  4. To obtain a curve fit to any of the graphs, select Analyze, then Automatic Curve Fit, then Sine. 

  5. Save your file with the name L20-3b-alias.cmbl. Upload it to the corresponding Moodle assignment now. You will need to use this file later for an assignment.

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