Fundamental Frequency

The fundamental frequency, or just the fundamental, is the lowest frequency of a periodic waveform. In Music Theory, the fundamental is the musical pitch of a note that is perceived as the lowest partial present.

In mechanical systems

For a single degree of freedom oscillator, like a mass-spring system, the natural frequency of oscillation depends on two quantities: mass and stiffness (provided the system is undamped)

\(\large \omega_0 = \sqrt{\dfrac{k}{m}}\),

where:
\(\large k\) is the stiffness of the string
\(\large m\) is the mass of the body
\(\large \omega_0\) is the natural frequency in rad/s

In Modal Analysis, the frequency of the 1st mode is the fundamental frequency.
This is also expressed as:

\(\large f_0 = \dfrac{1}{2l} \sqrt{\dfrac{T}{\mu}}\),

where:
\(\large f_0\) is the natural frequency
\(\large l\) is the length of the string
\(\large \mu\) is the mass per unit length of the string
\(\large T\) is the tension on the string