Find Amplitude of Glider in Air-Track Oscillation

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Homework Statement

An air-track glider attached to a spring oscillates between the 9.23 cm mark and the 50.23 cm mark on the track. The glider completes 27 oscillations in 44.7 s. angular frequency of the glider? (in rad/s)
3.7933
what is the amplitude of the glider?

Homework Equations

x=Acos(wt+ro)

The Attempt at a Solution

I considered that at x=9.23 the amplitude was zero and so is ro.
Hence, x=50.23 would equal just 50.23 cm=Acos(3.79(44.7)). But A turned out to be negative. What am I doing wrong? How do I solve this problem? Thank you in advance.

 

[dx]

What is the center of oscillation here? The amplitude is the maximum distance from the center that the glider reaches.

 

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Would it be half the distance the glider travels which is 20.5 cm?

 

[dx]

Correct.

 

[Liketothink]

It still gives me a negative number if I do .205/((cos(3.79*44.7)).

 

[dx]

Negative number for what?

 

[Liketothink]

For the amplitude A.

 

[dx]

You just said the amplitude was 20.5 cm, which is correct.

 

[Liketothink]

OH! Ok I get it. Thank you very much.

 

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Could you help me with this one too. It's about amplitude but I'm equally lost in that one as well.

https://www.physicsforums.com/showthread.php?t=320328