How Do You Calculate the Maximum Speed of a Speaker in Simple Harmonic Motion?

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SUMMARY

The maximum speed of a speaker in simple harmonic motion can be calculated using the formula for maximum speed, which is v_max = A * ω, where A is the amplitude and ω is the angular frequency. In this case, the amplitude is 0.8 m and the angular frequency ω is derived from the spring constant k and mass m using the equation ω = (k/m)^(1/2). Given the mass of the speaker is 90.0 g, the correct maximum speed is determined to be 8.43 m/s.

PREREQUISITES
  • Understanding of simple harmonic motion principles
  • Knowledge of angular frequency calculation
  • Familiarity with differentiation in calculus
  • Basic physics concepts related to mass and spring constants
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  • Study the derivation of the maximum speed formula in simple harmonic motion
  • Learn about the relationship between spring constant and mass in oscillatory systems
  • Explore differentiation techniques for finding velocity from position functions
  • Investigate practical applications of simple harmonic motion in real-world systems
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Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators looking for examples of simple harmonic motion calculations.

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Homework Statement



A loud speaker is connected to a string (spring constant k = N/m). The speaker moves back and forward in simple harmonic motion with an Amplitude of 0.8m. The frequency of an oscillation for amass on a string is w = (k/m)^1/2. The mass of the speaker is 90.0g.

What is the maximum speed of the speaker in m/s?

Homework Equations



Not sure which is the relevant in this situation.

The Attempt at a Solution



I found the value of w = 10.54.., however I'm not sure where to go from there. Thinking about this all week but can't work it out. The answer is 8.43m/s but how I should get this I am not sure. Any help would be really appreciated. Thanks
 
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Welcome to PF!

mark051 said:
A loud speaker is connected to a string (spring constant k = N/m). The speaker moves back and forward in simple harmonic motion with an Amplitude of 0.8m. The frequency of an oscillation for amass on a string is w = (k/m)^1/2. The mass of the speaker is 90.0g.

What is the maximum speed of the speaker in m/s?

Hi mark051! Welcome to PF! :smile:

(have a square-root: √ and an omega: ω :wink:)

The sine (or cosine) equation will give you the position of the end of the spring …

then differentiate it to give the velocity! :wink:
 

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