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GeorgesOatesLarsen / Physics-GRE-Testgen

command line (python) LaTeX physics GRE test generator
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ETS2017 Problem 3 #6

Open GeorgesOatesLarsen opened 4 years ago

GeorgesOatesLarsen commented 4 years ago

Inspiration:

Two simple pendulums A and B consist of identical masses suspended from strings of length L_A and L_B, respectively. The two pendulums oscillate in equal gravitational fields. If the period of pendulum B is twice the period of pendulum A, which of the following is true of the lengths of the two pendulums? (A) L_B = 1/4L_A (B) L_B = 1/2L_A (C) L_B = L_A (D) L_B = 2L_A (E) L_B = 4L_A

GeorgesOatesLarsen commented 4 years ago

We are dealing with the small angle pendulum formula, here: T = 2 pi sqrt(L/g)

We can do something very similar to ETS2017 P1, here. We will select which of the two variable ratios to give, and which one the user must find. The ratios must be selected so that L/g is a perfect square. This can be accomplished by selecting the squares of friendly fractions. All AB statements should have randomized order.

There will be a 50% chance that the masses of A and B are not identical, but disparate. This is useless information! But it will serve to nail that point into a user's head.