Calculating Spring Constant for Horizontal Oscillation of a Mass

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SUMMARY

The discussion focuses on calculating the spring constant for a 2.5 kg mass oscillating horizontally with a frequency of 1.0 Hz. The user attempts to derive the spring constant using the formula for the period of oscillation, \( T = 2\pi\sqrt{\frac{m}{k}} \). After manipulating the equation, the user arrives at a spring constant of approximately 98.7 N/m. The calculation is confirmed to be correct, demonstrating the application of the formula in determining the spring constant for a mass-spring system.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Familiarity with the formula for the period of oscillation
  • Basic knowledge of mass and frequency relationships in oscillatory motion
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Study the derivation of the period of oscillation for different mass-spring systems
  • Explore the effects of varying mass on the spring constant
  • Learn about energy conservation in oscillatory motion
  • Investigate the damping effects on oscillation in real-world applications
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators looking for practical examples of spring constant calculations.

cfalvo
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Homework Statement


Consider a 2.5kg mass oscillating at the end of a spring, with the frequency of 1.0Hz. The motion of the mass extends through 0.04m.


Homework Equations


Determine the spring constant-




The Attempt at a Solution



I can't find the right equation to set up this problem appropriately. The closest thing I could muster up was:

period=t= 2pi[tex]\sqrt{}[/tex]m/k
1=2pi[tex]\sqrt{}[/tex](2.5/k)
(1/2pi)=[tex]\sqrt{}[/tex](2.5/k)
(0.1592)(0.1592)=2.5/k
0.02533=k2.5
=98.6971(n/m)

-I'll bet good money I applied that equation wrong.
 
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That looks correct me.
 

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