26) This question asks about a pendulum with a mass M and length L. We want to find which answer choice is correct. All the answer choices are related to the period or frequency of the pendulum.
The problem specifies that the pendulum undergoes small oscillations, which means using the small-angle approximation we would find this equation for the period and frequency of this pendulum.
Now, considering these equations, we can go through the answer choices.
Choice A: The equation above shows that the amplitude of the oscillation is unrelated to the frequency of the oscillation. This choice is not correct.
Choice B: For the same reason as choice A, this cannot be a correct answer. Additionally, as you may be able to tell from the equation above, the period is the reciprocal of the frequency, so they are both unrelated to the amplitude.
Choice C: The equation for frequency doesn't include the mass of the pendulum bob. So this answer choice is correct.
Choice D: This choice is incorrect because we can see in the equation that as the length of the pendulum is changed, the frequency would as well.
Choice E: This is a tricky answer choice, at first look, if you were going through the questions very quickly, you might think that the frequency is inversely proportional to the length. However, this is not correct. The frequency is inversely proportional to the square root of the length. This means that if the length is increased by some factor c. the frequency would be decreased by a factor root(c).
Answer: C
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