Name _________________________
Simple Harmonic Motion Part 3
1.) Bring up your wave on the calculator. Put time on the x and displacement (distance) on the y. From your wave calculate the period (T) and the frequency (f)
T____________
f____________
2.) We can now write an mathematical equation relating the position as a function of time. Type the following formula into your equation editor.
3.) A stands for the amplitude of the wave to get A, Trace to the highest point on the crest of the wave and then to the lowest point on the trough of the wave. Subtract the y values and divide by 2.
A= _________
4.) W if you remember stands for angular velocity (w) which is equal to q/T. Since q is equal to 2p radians and the mode of our calculator is in radians the formula becomes 2p/T. Calculate W
W________________
5.) D stands for the vertical phase shift. To find D trace to the highest point on the crest of the wave and then to the lowest point on the trough of the wave. Add the y values and divide by 2. This will get you the middle line of the wave. Calculate D
D_________
6.) To aid in seeing if you calculated D correctly place the value of D in Y2 on your calculator and graph. It should appear in the middle of your wave. See pics below:
7.) C stands for the phase shift (horizontal). If we want to use a cosine function then the crest of the wave should be at its peak at time = 0. See pic below.
8.) From the middle of the function we know (WX + C). C can be found by tracing the first peak and writing down the x value
Set this x value = -C/W. Solve for C. (C is negative because we want to shift the wave left) In essence this shifts the wave left. Calculate C
C __________________
9.) Next store the values for A, W, C, and D in your calculator. Enter the value then STO --> then the letter. See pic.
10.) Erase the data from Y2 and hit graph. If everything goes well your equation should match your existing graph. If not you may have to slightly adjust one of the factors.
11.) Take a light probe and connect it to your calculator. Start the EasyData application. Hold the probe about 3 feet from a fluorescent light bulb. Calculate all of the values above and graph the wave. Answer the assigned questions and show your graph, equation, and matched graph to your instructor.