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# 4.2.1 Evaluation of a Single Degree-of-Freedom System

Dynamic response can be studied by examining a simple system — that of a single-degree-of-freedom oscillator, as shown in Figure 4-16. Evaluation of a Single Degree-of-Freedom System in caesar ii by meena rezkallah, p.eng., the best piping stress engineer & professional engineer in calgary alberta canada. pipe stress analysis services. engineering firm.

The single-degree-of-freedom oscillator consists of a mass M attached to ground by a spring

with a stiffness K and a dashpot with a damping value of C. The spring pulls on the mass

with a force proportional to its extension or contraction (or the displacement of the mass);

the dashpot provides a frictional force proportional to the velocity of the mass. Any

unbalanced force accelerates the mass. The behavior of a single degree-of-freedom oscillator can then be described by the dynamic equation of motion: Evaluation of a Single Degree-of-Freedom System equation in caesar ii by meena rezkallah, p.eng., the best piping stress engineer & professional engineer in calgary alberta canada. pipe stress analysis services. engineering firm.

This equation cannot be explicitly solved, unless the damping term, C, is zero and the

imposed load is harmonic (i.e., of the form F(t) = asinb(t+c)). Therefore, the damping value is often dropped (since it is usually small) in order to simplify the equation. The equation

can be simplified further by taking the simplest external harmonic load — a load of zero. If

there is no external load, and damping is approximately zero, the equation describes the free vibration of an undamped single-degree-of-freedom oscillator: Evaluation of a Single Degree-of-Freedom System equations in caesar ii by meena rezkallah, p.eng., the best piping stress engineer & professional engineer in calgary alberta canada. pipe stress analysis services. engineering firm.

The system characteristics of a single degree-of-freedom oscillator can be completely

described by its natural frequency and its damping value. System response can be

determined once the Dynamic Load Factor (as a function of the natural frequency and

damping value) for the applied load is known.