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Figure 1: The damped oscillation for example 1. Case (ii) Overdamping (distinct real roots) If b 2 > 4mk then the term under the square root is positive and the char
An example of a critically damped system is the shock absorbers in a car. It is advantageous to have the oscillations decay as fast as possible. Here, the system does not oscillate, but asymptotically approaches the equilibrium condition as quickly as possible.
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.
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.
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.
Critically-damped systems will allow the fastest return to equilibrium without oscillation. Response of an critically-damped system. The solution for a critically-damped system is:
An example of a critically damped system is the shock absorbers in a car. It is advantageous to have the oscillations decay as fast as possible. Here, the system does not oscillate, but asymptotically approaches the equilibrium condition as quickly as possible.
