Simple harmonic motion and frequency; answer disagrees from answer key

[clairez93]

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.

 

[Doc Al]

I'd say that you are correct and the answer key is wrong.