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Damping is a frictional force, so it generates heat and dissipates energy. When the damping constant b is small we would expect the system to still oscillate, but with decreasing amplitude as its energy is converted to heat.
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.
Figure 2 shows the response of the series RLC circuit with L=47mH, C=47nF and for three different values of R corresponding to the under damped, critically damped and over damped case. We will construct this circuit in the laboratory and examine its behavior in more detail. (a) Under Damped. R=500Ω (b) Critically Damped. R=2000 Ω (c) Over Damped.
Critically damped and overdamped responses do not oscillate, but rather asymptotically approach steady-state. The roots of the characteristic equation are referred to as the poles.
1.1 Drag and general Damping Forces. To achieve our objective of finding a more accurate model for oscillatory phenomena, we need to first find the correct Newton’s second law equation for such systems. Thus we need to better determine the forces acting on our oscillating object.
The response of a single-degree-of-freedom system to a step input depends critically on the damping in the system. There is a critical damping value for the system. Above critical damping value, the response is an exponential decay.
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.
