Editing Fundamental frequency (section)

== Mechanical systems ==
Consider a spring, fixed at one end and having a mass attached to the other; this would be a single degree of freedom (SDoF) oscillator. Once set into motion, it will oscillate at its natural frequency. For a single degree of freedom oscillator, a system in which the motion can be described by a single coordinate, the natural frequency depends on two system properties: mass and stiffness; (providing the system is undamped). The natural frequency, or fundamental frequency, {{var|ω}}<sub>0</sub>, can be found using the following equation:

{{block indent|1=<math> \omega_\mathrm{0} = \sqrt{\frac{k}{m}} \, </math>}}

where:
* {{var|k}} = [[stiffness]] of the spring
* {{var|m}} = mass
* {{var|ω}}<sub>0</sub> = natural frequency in radians per second.

To determine the natural frequency in Hz, the omega value is divided by 2{{var|[[Pi|π]]}}. 
Or:

{{block indent|1=<math>f_\mathrm{0} = \frac{1}{2\pi} \sqrt{\frac{k}{m}} \,</math>}}

where:
* {{var|f}}<sub>0</sub> = natural frequency (SI unit: hertz)
* {{var|k}} = stiffness of the spring (SI unit: newtons/metre or N/m)
* {{var|m}} = mass (SI unit: kg).

While doing a [[modal analysis]], the frequency of the 1st mode is the fundamental frequency.

This is also expressed as:

{{block indent|1=<math>f_\mathrm{0} = \frac{1}{2l} \sqrt{\frac{T}{\mu}} \,</math>}}

where:
* {{var|f}}<sub>0</sub> = natural frequency (SI unit: hertz)
* {{var|l}} = length of the string (SI unit: metre)
* {{var|μ}} = mass per unit length of the string (SI unit: kg/m)
* {{var|T}} = tension on the string (SI unit: newton)<ref>{{Cite web|url=https://www.wirestrungharp.com/material/strings/about_string_calculator/|title=About the String Calculator|website=www.wirestrungharp.com}}</ref>