Calculate Force Constant of Spring: Vibrational Frequency 7.00/s

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SUMMARY

The discussion focuses on calculating the force constant of a spring with two 3.5 g masses attached, given a vibrational frequency of 7.00 s-1. The correct formula for the force constant (k) is k = (2πcω)²μ, where μ is the reduced mass. The participant expresses confusion about converting the frequency into the appropriate units for the formula and questions the relevance of the provided equations, which pertain to optics rather than mechanics.

PREREQUISITES
  • Understanding of simple harmonic motion (SHM)
  • Familiarity with the concept of reduced mass
  • Knowledge of wave number and its units (1/cm)
  • Basic grasp of energy equations in quantum mechanics
NEXT STEPS
  • Learn how to convert vibrational frequency into wave number (1/cm)
  • Study the derivation and application of the force constant formula for springs
  • Explore the relationship between mass, frequency, and energy in SHM
  • Investigate the differences between mechanical and optical equations in physics
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and quantum mechanics, as well as educators seeking to clarify concepts related to simple harmonic motion and spring constants.

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Homework Statement



Two 3.5 g masses are attached by a spring has a vibrational frequency of 7.00 s-1. Calculate
(a) the force constant of the spring; (b) the zero point energy; (c) the potential energy if the
maximum displacement is 0.5 cm.

Homework Equations


k=((2πcω)^2)μ
E=(1/2)hcw

(NOTE: The omega(w) in the formulas has a ~ over the top representing wave number which has the units 1/cm)

The Attempt at a Solution



The question gave me the vibrational frequency of 7.00/s. I don't how to put the frequency in terms of 1/cm so i can plug it into the force constant formula
 
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These don't look like the right equations for the problem. They're from optics, not mechanics. Do you not have an equation for the SHM of a mass on a spring?
 

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