This spring mass calculator finds the natural (resonant) frequency and period of a spring-mass system from the spring stiffness and the attached mass. Enter both values above.
Formulas
Frequency f = (1 ÷ 2π) × √(k ÷ m) Period T = 2π × √(m ÷ k)
- k — spring stiffness (N/m), m — mass (kg)
Example
k = 200 N/m, m = 0.5 kg: f = (1/2π)√(400) = 3.18 Hz, period T = 0.314 s.
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Frequently Asked Questions
How do I find the natural frequency of a spring?
Take the square root of stiffness over mass, divided by 2 pi: f = (1/2pi) x sqrt(k/m).
What is the period of a spring-mass system?
It is 2 pi times the square root of mass over stiffness, the inverse of the natural frequency.
Does a heavier mass lower the frequency?
Yes. More mass lowers the natural frequency; a stiffer spring raises it.