PHY 201
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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Randomized Problems: Assignment 2, Problem 2. Follow same directions as for Assignment 2, Problem 1.
This problem is from the above section on the assignments page for the physics 201 course. I'm not sure where in the class notes there has been anything that goes over that type of problem.
For a certain pendulum, periods of T = .91, 1.291681, 1.58539 and 1.83345 seconds are observed for respective lengths L = 7, 14, 21 and 28 units.
* Determine whether the transformation T -> T2 or T -> T3 linearizes the function better.
* Determine the equation of the resulting straight line, and solve the equation for T.
* Use your equation to determine the period of a pendulum whose length is 51.19815 units.
* Use your equation to determine the length of a pendulum whose period is 2.424873 seconds.
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I'm not quite sure how to do that problem. Also if there is examples on the site, I cannot find them anywhere.
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This is done in the Class Notes and it's worth knowing how to do.
However I don't penalize this problem if it occurs on a test.
I will respond tomorrow with the details of how to solve problems of this nature, for your reference if you should choose to take a look at it (which you won't be obligated to do).
Briefly, if plot T vs. L you will get a curve that decreases at a decreasing rate.
However if my mental calculations are correct, if you square the T values and plot them against the L values, you will get something close to a straight line (squared T values very approximately equal to .8, 1.6, 2.6, 3.7 vs. equally spaced L values result in a straight line).
That line will have equation T^2 = m * L + b, where m is the slope of that graph and b the vertical intercept. You can determine these quantities from the graph and fill them in. This gives you an equation you can solve for T if you know L, or for L if you know T.
Details tomorrow.