How do you measure resonance frequency?

Question

Is there a way to measure or calculate the resonance frequency of an object?

Answer 1

If you have an arrangement where there is a restoring force k and a mass m then you can set up a differential equation. The solution is

F = 1/(2 Pi) sqrt(K/m)

if K in newtons per meter
and m is Kg
then F will be Hz

Answer 2

One way is to hit it with an "impulse". Mathematically that works out to a pulse of infinite amplitude, zero width, having an energy of unity. The object will "ring" at its resonant frequency. Practically, a good sharp pulse will do in electronics. For mechanical things, use a good hammer swat. Works with bells. The latter is the exact physical example of the impulse response producing the characteristic response of the system under test.