A single degree of freedom (SDOF) system is a mechanical or structural model where the motion is described by only one coordinate (π₯(π‘) or π(π‘)) at any time.
It represents simple vibrations, such as a swaying building or a car suspension, where only one main direction of movement matters.Β
An undamped SDOF system is said to undergo free vibration when it oscillates only under an initial disturbance with no external forces acting afterwards.
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- The amplitude of motion remains constant with time.
- The system vibrates at its natural frequency fn
- It is used as the fundamental building block for analyzing more complex dynamic, structural, or mechanical vibrations.Β
Frequency (π) and angular frequency (π) are directly proportional, related by the formula π=2ππ. While frequency measures the number of cycles per second (in Hertz, Hz), angular frequency measures the rate of phase change in radians per second (rad/s), representing the angular rotation of a phasor (a rotating vector) over time.Β
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When a damper is added to the system it results in an exponential decrease in amplitude with time.
The frequency of oscillation known as the damped natural frequency is constant and almost the same as the natural frequency fn.
The damped natural frequency decreases slightly for an increase in damping.
The damping ratio (π) is a dimensionless parameter, usually denoted by the Greek letter zeta, that quantifies how oscillations in a SDOF system decay after a disturbance. It represents the ratio of actual damping (π) to critical damping (πc):
