Total distance in simple harmonic motion

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Homework Help Overview

The problem involves a mass oscillating in simple harmonic motion along the x-axis, with specific parameters such as the number of cycles and vibrational amplitude. The original poster seeks to determine the total distance traveled by the mass over these cycles.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster successfully calculates the frequency but expresses confusion regarding the calculation of total distance traveled. Some participants clarify the relationship between cycles and amplitude, while others attempt to break down the calculations for clarity.

Discussion Status

Participants are actively engaging in the discussion, with some providing breakdowns of the calculations involved. There is a focus on clarifying the reasoning behind the total distance formula, though no consensus has been reached regarding the original poster's understanding.

Contextual Notes

The discussion includes an assumption about the formula for total distance in simple harmonic motion, specifically relating to the amplitude and number of cycles. There may be constraints related to the original poster's understanding of the concepts involved.

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Homework Statement



A mass oscillates along the x-axis in simple harmonic motion. It goes through 200 cycles in 10 seconds and its vibrational amplitude is 0.020 m. What is the frequency, in hertz, and the total distance traveled, in meters, by the mass in the 200 cycles?


Homework Equations





The Attempt at a Solution



I got the frequency but cannot understand how to get the total distance.
The explanation just says "one cycle goes through distance 4A. 200 * 4A = 800A = 16m". Can someone explain this to me please?
 
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A is the Amplitude.
 
Yes I know that, but I just don't understand how 800A equals 16.
 
800*.02 = (8*100) * (2/100) = (100/100)*(8*2) = (1)*(16) = 16
 

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