Mechanical Systems
Consider a beam, 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 radian frequency, ωn, can be found using the following equation:
Where:
k = stiffness of the beam
m = mass of weight
ωn = radian frequency (radians per second)
From the radian frequency, the natural frequency, fn, can be found by simply dividing ωn by 2π. Without first finding the radian frequency, the natural frequency can be found directly using:
Where:
fn = natural frequency in hertz (cycles/second)
k = stiffness of the beam (Newtons/meter or N/m)
m = mass at the end (kg)
while doing the modal analysis of structures and mechanical equipments, the frequency of 1st mode is called fundamental frequency.
Read more about this topic: Fundamental Frequency
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