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Learning Objectives. Learn to analyze a general second order system and to obtain the general solution. Identify the over-damped, under-damped, and critically damped solutions. Convert complex solution to real solution. Suspended “mass-spring-damper” equivalent system.
Polynomial A(s) is stable (i.e. all roots of A(s) have negative real parts) if there is no sign change in the first column. The number of sign changes in the first column is equal to the number of roots of A(s) with positive real parts. Examples: A(s) = a0s2 + α1 s + α2.
Effect of Damping Ratio on System Response . Depending on whether the quantity (ζ 2 −1) is negative, zero, or positive, the system is underdamped, critically damped, or overdamped, respectively. Underdamped: When this quantity is negative (ζ<1), the system is said to be underdamped. This is, by far, the most common case for structural systems.
This document discusses the response of a second-order system, such as the mass-spring-dashpot shown in Fig. 1, to a step function. The modeling of a step response in MATLAB and SIMULINK will also be discussed. Fig. 1. Single-degree-of-freedom mass-spring-dashpot system.
The response of a system to an impulse looks identical to its response to an initial velocity. The impulse acts over such a short period of time that it essentially serves to give the system an initial velocity. Fig. 3 shows the impulse response of three systems: under-damped, critically damped, and over-damped.
The concept of logarithmic decrement for estimation of the viscous damping ratio from a free-response vibration test. The free vibration response of an underdamped 2nd order viscous system (M,K,D) due to an initial displacement Xo is a decay oscillating wave with damped natural frequency (ωd).
9 Μαΐ 2023 · Critically damped. Overdamped systems. 4.1 Introduction. In this chapter, analysis and characterization of responses of mechatronics and measurement systems under static and dynamic conditions are presented. Details of first-order and second-order system characteristics and experimental determination of these characteristics are covered.
