Single Degree-of-Freedom Systems

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	SDOF Vibration
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Calculators

Definition

The simplest vibratory system can be described by a single mass connected to a spring (and possibly a dashpot). The mass is allowed to travel only along the spring elongation direction. Such systems are called Single Degree-of-Freedom (SDOF) systems and are shown in the following figure,

Simulate!

Equation of Motion for SDOF Systems

SDOF vibration can be analyzed by Newton's second law of motion, F = m*a. The analysis can be easily visualized with the aid of a free body diagram,

The resulting equation of motion is a second order, non-homogeneous, ordinary differential equation:

with the initial conditions,

The solution to the general SDOF equation of motion is shown in the damped SDOF discussion.

Simulate Vibrations With IP2000!

You can easily simulate the motion of spring/mass/damper systems using the powerful software package Interactive Physics from MSC Working Knowledge. It provides an easy-to-use, interactive, and discovery-oriented platform where thought experiments can be quickly reduced to full simulation results.