Oscillating Springs: Finding Frequency w/ k1, k2, & m

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SUMMARY

The discussion focuses on calculating the frequency of vibrations for a mass m attached to two springs with stiffness constants k1 and k2. The relevant formula for frequency is f = (1/2π)√(k/m), but the challenge lies in determining how to combine the spring constants k1 and k2. The solution involves equating the forces of the two springs to derive a combined spring constant, which is essential for accurately calculating the frequency of the system.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Familiarity with the formula for frequency of oscillation
  • Basic knowledge of mechanical vibrations
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Research how to combine spring constants in series and parallel configurations
  • Learn about the concept of effective spring constant
  • Explore the derivation of frequency formulas for oscillating systems
  • Study energy conservation principles in spring systems
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillations, as well as educators looking for examples of spring dynamics in real-world applications.

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Homework Statement



I've had some problems trying to work through this problem:

Two springs of stiffness k1 and k2 are attached in succession to a mass m. What is the frequency of vibrations in terms of the spring stiffness k1 and k2 and the mass m?

Homework Equations



f=(1/2pi)sqrt(k/m)

I think that is the only relevant equation, but I am not entirely sure.

The Attempt at a Solution



I am confused at weather or not I need to multiply or add the two spring constants. Or, if I need to make two separate equations with the frequencies being constant in both equations.

I tried to relate it to the energy of a spring, but I didn't have a displacement so that equation would not work.

Any help would be greatly appreciated, Thanks!:smile:
 
Physics news on Phys.org
try 2 dispalcement variables
the end of the first spring
the end of the 2nd spring

write down the force vs distance equation of each spring & so find the expression for the 2 combined by equating the force
 

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