The natural frequency, also known as the fundamental frequency, refers to the number of times a given event will happen in a second. This can be the number of times an instrument resonates, or the number of times a rod vibrates. If the natural frequency is exceeded, an object can break. For example, the Tacoma Narrows Bridge vibrated past its natural frequency and collapsed.
Calculating the Natural Frequency
Determine the mass of the weight on the end of the rod by placing it on the scale. Don not include the rod. For example, a mass might by five kilograms. This will be m in the equation.
Determine the stiffness based on what the material is by consulting a stiffness table. For example, a plastic rod might have a stiffness of twenty Newton meters. This will be k in the equation.
Plug the values for mass and stiffness into the equation natural frequency equals the square root of the quantity of stiffness divided by mass divided by two pi. From the example above, divide twenty Newton square meters by five kilograms to get four hertz squared. Take the square root and you get two hertz. Divide two hertz by two pi and you one over pi, or about 0.32 hertz.
F = (1 / 2?) * ? (k / m)
Be sure to use the same set of units for each step. For example, if you measure the mass in kilograms, you must use Newton meters for the stiffness.
The unit for natural frequency is hertz, or occurrences per second, so if the natural frequency is five hertz, that means it occurs five times per second.