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

In summary, the amplitude of a particle undergoing Simple Harmonic Motion represents the maximum distance it travels from its equilibrium position. One period is the time it takes for the particle to make one full oscillation. Therefore, the total distance traveled in one period would be twice the amplitude, resulting in a distance of 1.36m.
  • #1
meganw
97
0

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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  • #2
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?
 
  • #3
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!
 

1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which a system moves back and forth around an equilibrium point with a constant amplitude and a constant period. It can be described by a sine or cosine function.

2. What is the formula for simple harmonic motion?

The formula for simple harmonic motion is x(t) = A sin(ωt + φ), where A is the amplitude, ω is the angular frequency, t is time, and φ is the initial phase angle.

3. How is simple harmonic motion different from other types of motion?

Simple harmonic motion is different from other types of motion because it is a type of oscillation that is caused by a restoring force that is proportional to the displacement from equilibrium. This results in a sinusoidal motion with a constant amplitude and period.

4. What are some examples of simple harmonic motion?

Some examples of simple harmonic motion include a mass on a spring, a pendulum, and a vibrating guitar string.

5. How is simple harmonic motion used in real life?

Simple harmonic motion is used in many real-life applications, such as in clocks, musical instruments, and earthquake-resistant buildings. It is also used in engineering and physics to model and analyze systems that exhibit periodic motion.

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