Solving Spring Oscillations Homework: Stretched Distance d

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SUMMARY

The discussion revolves around calculating the stretched distance (d) of a spring when a mass of 0.35 kg is attached. The participant calculated the period (T) to be approximately 0.489 seconds based on 100 oscillations in 48.9 seconds. Using the formula T = 2π(√(m/k)), they determined the spring constant (k) to be 3.45 N/m. However, the calculated distance was approximately 1 meter, while the correct answer provided by the teacher is 5.94 cm, indicating a miscalculation in the application of the formulas.

PREREQUISITES
  • Understanding of harmonic motion and oscillations
  • Familiarity with Hooke's Law (F = kx)
  • Knowledge of the relationship between period and frequency
  • Basic algebra for manipulating equations
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  • Review the derivation of the formula for the period of a mass-spring system
  • Learn about the implications of spring constant (k) in oscillatory motion
  • Study the effects of mass on the oscillation frequency
  • Explore common mistakes in calculations involving oscillations and springs
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Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators looking for examples of common calculation errors in spring dynamics.

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Homework Statement


When a mass of 0.35 kg is attached to a vertical spring and lowered slowly, the spring stretches a distance of d. The mass is now displaced from its equilibrium position and undergoes 100 oscillations in 48.9 seconds. WHat is the stretched distance d?

Homework Equations


Number of oscillations/Time = Period (T)
T = 2pi ([tex]\sqrt{m/k}[/tex])
F=kx

The Attempt at a Solution


I found by doing 100/48.9, the period is around 2 oscillations per second.
Using the second equation I figured out that k=3.45 by plugging it all the other variables. Then i know that the F=mg. So mg is 3.43.
3.43/3.45 = x (distance)
The distance comes out to around 1. But my teacher says that 5.94 cm...what did i do wrong?
 
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the period is supposed to be 48.9/100 s
 

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