Quick Question - Simple Harmonic Motion - (I think I just need a formula)

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SUMMARY

The discussion revolves around calculating the total distance a particle travels during one period of Simple Harmonic Motion (SHM) with an amplitude of 0.34 m. The key formula used is x = A sin(wt + θ), where A represents amplitude. The participant realizes that the total distance traveled in one complete oscillation is double the amplitude, leading to a final answer of 1.36 m. This understanding clarifies the relationship between amplitude and distance in SHM.

PREREQUISITES
  • Understanding of Simple Harmonic Motion (SHM)
  • Familiarity with the formula x = A sin(wt + θ)
  • Knowledge of amplitude in oscillatory motion
  • Basic concepts of oscillation and equilibrium position
NEXT STEPS
  • Study the properties of Simple Harmonic Motion in detail
  • Learn about the energy transformations in SHM
  • Explore the concept of damping in oscillatory systems
  • Investigate real-world applications of SHM, such as in springs and pendulums
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators looking to enhance their teaching of Simple Harmonic Motion concepts.

meganw
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Homework Statement



If a particle undergoes Simple Harmonic Motion with amplitude 0.34 m, what is the total distance it travels in one period?

Homework Equations



x=Asin(wt+theta)

The Attempt at a Solution



I know A, (.34), yet it seems like this problem doesn't give me nearly enough information to find anything else! I think I just need a different formula...or perhaps knowledge of another concept. We just started this unit so it might be just something really simple that I'm missing. Thank you!
 
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The amplitude is the maximum distance the spring is compressed or stretched from its equilibrium position. In an ideal spring, which is one that represents Simple Harmonic Motion, if one were to stretch (or compress) a spring to a certain amplitude and let go, the spring would oscillate back and forth, with its maximum distance from the equilibrium position being the amplitude. One period is basically the time it takes for the spring to make one full oscillation, which is basically when the spring makes a full trip back and forth...using that, how much would you think the spring travels in one period?
 
Oh! Okay, I didn't even realize that's what amplitude meant! Thanks. In an ideal spring, that means it would just perfectly double the distance (of going back and forth once). =) Thanks!

So that gives me the correct answer of 1.36m. Thank You!
 

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