SDOF

SDOF stands for Single Degree of Freedom. It is a fundamental concept in physics and engineering, particularly in the study of vibrations and structural dynamics. A system is considered to be SDOF if its motion can be completely described by a single coordinate. This means that at any given time, the position and motion of the entire system can be uniquely determined by the value of this single variable.

Simple examples of SDOF systems include a mass attached to a spring, or a pendulum with small oscillations. In these cases, the single degree of freedom can represent the displacement of the mass from its equilibrium position or the angular displacement of the pendulum. More complex systems are often approximated as SDOF systems for analysis purposes, simplifying the problem without losing essential characteristics. This simplification is useful in understanding the basic behavior of vibrations, such as natural frequency and damping.

The equation of motion for an undamped SDOF system is typically represented by a second-order linear differential equation: m(d^2x/dt^2) + kx = 0, where 'm' is the mass, 'k' is the stiffness, and 'x' is the displacement. When damping is included, the equation becomes m(d^2x/dt^2) + c(dx/dt) + kx = F(t), where 'c' is the damping coefficient and F(t) is an external force. Analyzing these equations allows engineers to predict how structures will respond to dynamic loads like earthquakes or wind.