Q:

Natural frequency of spring-mass system

We can found on internet videos or articles about resonance. For this they for e.g. take a system of two spring and mass in between. When they set force frequency to close to natural frequency. But from where they know the natural frequency of the system?

A:

You can find the natural frequency of such a system theoretically, if you know the stiffness of the springs. Refer:this example on wolfram.
How do you find the stiffness of the springs? Well... do experiments on simple pendulum, find the natural frequency from time period of oscillation, reverse calculate the stiffness of the spring as the mass of the test mass is known.
That was for the 2-spring-1-mass system. For general vibrating systems, one has to again do corresponding experiments (which involves high frequency oscillations, making observations difficult) to find the natural frequencies.

