Physics

Natural Frequency Calculator

Find the natural frequency of a spring-mass system.

Calculated Output

Natural frequency (Hz) 7.958

Angular frequency (rad/s) 50

Formula: f = (1 ÷ 2π)·√(k ÷ m)

Step-by-Step Breakdown

1. Values used:

2. Stiffness = 5,000 N/m

3. Mass = 2

5. Natural frequency = 7.958Hz

6. Angular frequency = 50rad/s

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The math behind it

f = (1/2π)·√(k/m). Stiffer springs and lighter masses vibrate faster.

k = 5000 N/m, m = 2 kg → about 7.96 Hz.

Why avoid resonance?

Driving a system at its natural frequency can build up dangerously large vibrations.