How Does Amplitude Affect Total Distance Traveled in SHM?

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In the discussion about how amplitude affects total distance traveled in simple harmonic motion (SHM), the main focus is on solving a physics homework problem involving a particle with an amplitude of 0.25m. The participant is confused about which formula to apply, as they feel they lack sufficient information. They mention several relevant formulas related to amplitude and velocity but are unsure how to proceed. The conversation highlights the need for clarity on the relationship between amplitude and total distance in one period, which is typically twice the amplitude in SHM. Ultimately, the participant seeks guidance on selecting the correct formula to calculate the total distance traveled.
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Vibrations and Waves - please help!

I'm having trouble with my physics homework. I can't seem to figure out which formula to use to solve a particular problem.

"If a particle undergoes SHM with amplitude 0.25m, what is the total distance it travels in one period?"

The formulas I have that deal with amplitude are:
V= \pmV{o}\sqrt{1 - x^{2}/A^{2}}

V=A\sqrt{k/m}

x=Acos2* \pi(frequency)t​
I don't know which formula to use because it seems like I don't have enough information for any of them. Could someone please tell me which formula to use and why?
 
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A=4(pi)r^2
so r=sqrt(A/4pi)

your A=0.25
so:
r=sqrt(0.25m/12.57)=.020m
 

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