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Simple Harmonic Motion Name: Data Table 1 Length (m) Time for 10 Swings (s) Period (s) Include Graph (See question 1A) 0.20 9.33 0.9327 0.40 13.19 1.3195 0.60 16.16 1.6160 0.80 18.67 1.866 1.0 20.86 2.0859 Data Analysis 1. Use the graphing software of your choice to create a graph of the period versus the length. The shape of the graph may be different than any other you have done. Do a curve fit on the graph as a power function. The resulting graph is a half-parabola around the x-axis. A. Include a screenshot of your graph in the space above. B. Describe the equation from the graph in a complete sentence. The graph seems to have a inverse relationship (hyperbola) but the thing is it’s around the x axis and not the y axis. But at the same time as length increases, so does the period because a pendulum with a longer length takes longer to cover the distance to swing from one side to the other. C. The square root of x can be written as x 1/2 . If the generic equation is y = kx 1/2 , give the specific equation using the actual variables in this data, instead of the generic "y" and "x." It could then be considered an inverse squared relationship of the graph. Y=2.0816*x^5 2. Examine your graph. A. What length pendulum would have a period of 1.0 s? 2.086mB B. What period would be produced by a pendulum 1.5 m long? 0.51s Questions: 3. The equation for the period of a pendulum is 𝑇 = 2π 𝐿 𝑔 A. How does your equation from 1C compare to the pendulum equation? The time period of the pendulum, T, is equal to 2pi times the square-root of L over g. frequency of the pendulum, which is the rate at which the pendulum swings back and forth. B. Use the pendulum equation to calculate the period of a 1.50 m pendulum. Remember that the value of "g" is 9.8 m/s 2 . Unless Otherwise Noted All Content © 2022 Florida Virtual School. FlexPoint Education Cloud ™ is a trademark of Florida Virtual School.