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Static deflection and frequency

If you know the static deflection $\delta$ a mass produces on its spring, you can find the natural frequency without knowing $k$ or $m$ separately. This follows because $k\delta = mg$ , which gives $k/m = g/\delta$ directly in the formula for $\omega_n$ .

\omega_n = \sqrt{g/\delta}

natural angular frequency from static deflection

Symbols

$\delta$	static deflection	m
$g$	gravitational acceleration	m/s²

Example

A static deflection of $\delta = 5$ mm:

$\omega_n = \sqrt{9.81/0.005} \approx 44.3$ rad/s.

Handy shortcut: just measure how much the spring sags under the load, not

k

and

m

separately.

Practise free vibrations for free →

← Springs in series and parallel · Damping ratio →

Part of Machine Dynamics and Vibrations: Free vibrations.