Spring Natural Frequency Calculator

Inputs

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Diameter of the spring wire.
mm
Center-to-center across the coil, usually outside diameter minus wire diameter.
mm
Coils that deflect and determine the spring rate.
Used to estimate wire length and spring mass. Closed and ground ends often add about two inactive coils.
Sets shear modulus for rate and density for spring mass.
Moving mass attached to the spring. Enter 0 to estimate spring-only frequency from effective spring mass.
kg
Fraction of spring wire mass added to the moving mass. A common one-end-fixed approximation is 1/3.
Cycle frequency to compare against the natural frequency.
Hz
Natural frequency divided by operating frequency target. 5 means keep operation at or below fn/5.

Results

Default result
Edit inputs
Natural frequency(f_n)
25.4Hz
Pass

Also computed

Max operating frequency(f_op,max)5.081Hz

fn divided by the target separation factor.

Frequency ratio(f_n/f_op)Pass5.081

Meets the entered 5:1 separation target.

Natural period(T)0.03936s

Angular frequency(omega_n)159.6rad/s

Spring rate(k)6.453N/mm

Spring mass(m_s)0.009917kg

Music wire

Method notes 5 notes
  • Spring rate uses k = G*d^4/(8*D^3*Na), with G from the selected spring material.
  • Wire length is approximated as pi*D*Nt, so spring mass uses wire cross-section area, helix circumference and material density.
  • Effective moving mass is m_eff = m_load + eta*m_s. A one-end-fixed spring with an attached mass often uses eta = 1/3.
  • Natural frequency is f_n = (1/(2*pi))*sqrt(k/m_eff), using k in N/m and effective mass in kg.
  • This is a lumped first-mode screen. Surge, damping, end constraints, preload, nonlinear/progressive coils, coil clash, fatigue, guides and test data need separate review.

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