5. Calculate Natural Frequency and Damping

Use the program FREQDAMP on your TI Graphing Calculator to calculate the natural frequency and damping of your model. You will need to read values from the graphs you saved from the Free-Vibration Decay experiment.

5.1 Recall Graphs

On your TI Graphing Calculator recall your clearest graph.

Press [DRAW] 2
       (to display the DRAW STO menu and select RecallPic)
Press 4 (to display VARS PIC menu)
Press 1,2,3,4,5 or 6 to recall your graph from Pic1, Pic2, Pic3, Pic4, Pic5, or Pic6
Press

5.2 Select Two Peaks

Choose two pairs of (x,y) coordinates from your graph which occur at different peaks, like the ones shown in the graphs. You can choose two positive peaks or two negative troughs.

These are artificially produced graphs to demonstrate how to use the program FREQDAMP.

Use the cursor and move it onto the first peak.

You can use ,, or to move the cursor around the graph.
If you want to move along the plotted line,
press TRACE and then move the cursor using or .

As you move the cursor around the graph, you will see the changing (x,y) coordinates displayed below the graph.

Write down the (x,y) coordinates for the peaks that you choose AND the number of complete cycles of oscillation between them.

Example:

Call the point with the lowest x-coordinate peak A and the other point peak B.

Remember, the x-coordinates are time and the y coordinates are acceleration.

From the graph above

Peak A:
Time (x) = 0.170 secs
Acceleration (y) = 0.719 m/sec/sec

Peak B:
Time (x) = 0.670
Acceleration (y) = 0.280 m/sec/sec

Number of cycles between two peaks=3

5.3 The Calculation

On your TI Graphing Calculator,

press
Enter the number before FREQDAMP
The calculator displays prgmFREQDAMP
Press

The program will start.

Follow the instructions on the calculator display.

You can exit the program at any time by pressing ON and then pressing the number before Quit (2 on the TI-82, 1 on the TI-83).

You will need to enter the time and acceleration for both peaks and also the number of cycles between them. If you have chosen troughs and have negative values for acceleration you should enter them using the key on your TI Graphing Calculator.

Try out the program using the values from the example graph.

The program will calculate the natural frequency and damping and display:

You can now use the Accurate Earthquake Mass Calculator to find out the mass you need to load each floor of your model.

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