Problem Statement
Given the mass m and stiffness k of an undamped SDOF system, find the system's natural frequency in both Hz and radians per second as well as the natural period of vibration.
Background
An undamped, linear single degree-of-freedom (SDOF) system can be visualized as a spring with stiffness k, fixed at one end and having a mass m attached to the other:
Once set into motion, the system will oscillate at its natural frequency, or fundamental frequency:
where the natural frequency is in radians per second.
The time required for the undamped system to complete one cycle of free vibration is the natural period of vibration of the system, , which has units of seconds:
A system executes cycles in 1 second. This is the natural cyclic frequency of vibration:
which has units of Hertz (Hz) or cycles per second. The term natural frequency of vibration applies to both and . They have the relationship:
Example
m = 10;
k = 2;
[wn,fn,Tn] = udSDOF(m,k)
wn = 5
fn = 0.7958
Tn = 1.2566
Solve

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Last Solution submitted on Feb 05, 2026

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Matthew Bolyard 宣余 宇轩 Lorenzo

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