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)

${\omega }_0=\sqrt{\frac{k}{m}}$,

where: $k$ is the stiffness of the string $m$ is the mass of the body ${\omega }_0$ 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:

$f_0=\frac{1}{2l}\sqrt{\frac{T}{\mu }}$,

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