Assignment2_RandomProblem_2

course Phy 241

My graph does not show on the form, if you need it to supplement my answer, I can email it to you. Just let me know.

Your work has been received. Please scroll through the document to see any inserted notes (inserted at the appropriate place in the document, in boldface) and a note at the end. The note at the end of the file will confirm that the file has been reviewed; be sure to read that note. If there is no note at the end, notify the instructor through the Submit Work form, and include the date of the posting to your access page.

This is done by creating a table. The table created is as follows:

Length(x) Period (y) y^2 y^3

4 0.29 0.0841 0.024389

8 0.40844 0.166823 0.068137

12 0.499034 0.249035 0.124277

16 0.575253 0.330902 0.190361

Now we must evaluate the difference between consecutive entries. Note this can be done only because the x values are also equally spaced apart. The table of y^2 seems to follow a pattern with about the same amount of difference each number, .08. This tells us that graphing x vs y^2 will give us a linearization.

Determine the equation of the resulting straight line, and solve the equation for T.

The graph can be drawn by hand and an equation can be determined by selecting two points other than the data points on a line of best fit and calculating the slope and y intercept. The equation will follow the y=mx+b format, where m is the slope y is y^2 and b is the y intercept. The graph will appear as follows:

Notice the equation generated in the top corner. This equation can also be done by hand as described above, but will be less accurate. The equation here should actually read y^2=0.0206x + 0.021. To obtain an equation to substitute our original values we must take the square root on both sides to yield, y=√(0.0206x + 0.021).

Use your equation to determine the period of a pendulum whose length is 14.50471 units.

Substituting x as 14.50471 we obtain approximately 0.54854

Use your equation to determine the length of a pendulum whose period is 1.220222 seconds.

Substituting y as 1.220222, we obtain a length of about 72.18.

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This looks good. Do remember to include a copy of the problem when you submit a Randomized Problem; in this case the details of the problem were implicit so I could tell what question you were answering.