Simple harmonic motion and frequency; answer disagrees from answer key

AI Thread Summary
The discussion centers on a problem involving a block attached to a spring oscillating in simple harmonic motion, with limits of motion at 10 cm and 50 cm. The correct amplitude is calculated as 20 cm, but there is confusion regarding the frequency. The individual initially calculated the period as 0.5 seconds, leading to a frequency of 2 Hz, while the answer key states the frequency is 4 Hz. The misunderstanding arises from the interpretation of the motion's cycle duration, with some participants agreeing that the answer key may be incorrect. The consensus suggests that the frequency should indeed be 4 Hz based on the motion's characteristics.
clairez93
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Homework Statement



A block attached to a spring oscillates in simple harmonic motion along the x axis. The limits of its motion are x = 10 cm and x = 50 cm and it goes from one of these extremes to the other in 0.25 s. Its amplitude and frequency are:

A) 40 cm, 2 Hz
B) 20 cm, 4 Hz
C) 40 cm, 2 Hz
D) 25 cm, 4 Hz
E) 20 cm, 2 Hz


Homework Equations



T = 1/f

The Attempt at a Solution



I got the amplitude correct by adding the limits and dividing by two to find the midpoint of the motion, which was 30 cm, which I took to be equilibrium. Then I subtracted 10 cm, one limit of motion, from 30 cm, equilibrium to get the amplitude of 20 cm.

The frequency is where I mess up. I multiplied .25s by 2, since I thought it takes .25 seconds to complete half the cycle; I thought it must go back to the same extreme to complete a cycle, and thus would take another .25s. I got .5s for the period and then took the reciprocal of .5 for a frequency of 2 Hz.

The answer key however says the answer is B, a frequency of 4 Hz. Is this a mistake of the answer key or on my part? I do not see why the frequency would be 4.
 
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I'd say that you are correct and the answer key is wrong.
 
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