It would be quite inconvenient if the needle oscillated about the new equilibrium position for a long time before settling. Damping forces can vary greatly in character.
Friction, for example, is sometimes independent of velocity as assumed in most places in this text. But many damping forces depend on velocity—sometimes in complex ways, sometimes simply being proportional to velocity.
Damping oscillatory motion is important in many systems, and the ability to control the damping is even more so. This is generally attained using non-conservative forces such as the friction between surfaces, and viscosity for objects moving through fluids.
The following example considers friction. Suppose a 0. Figure 4. The transformation of energy in simple harmonic motion is illustrated for an object attached to a spring on a frictionless surface. This problem requires you to integrate your knowledge of various concepts regarding waves, oscillations, and damping. To solve an integrated concept problem, you must first identify the physical principles involved.
Part 1 is about the frictional force. Part 2 requires an understanding of work and conservation of energy, as well as some understanding of horizontal oscillatory systems. Now that we have identified the principles we must apply in order to solve the problems, we need to identify the knowns and unknowns for each part of the question, as well as the quantity that is constant in Part 1 and Part 2 of the question.
Identify the known values. The work done by the non-conservative forces equals the initial, stored elastic potential energy. Identify the correct equation to use:.
The number of oscillations about the equilibrium position will be more than. This system is underdamped. For example, if this system had a damping force 20 times greater, it would only move 0. This worked example illustrates how to apply problem-solving strategies to situations that integrate the different concepts you have learned. The first step is to identify the physical principles involved in the problem. The second step is to solve for the unknowns using familiar problem-solving strategies.
These are found throughout the text, and many worked examples show how to use them for single topics. In this integrated concepts example, you can see how to apply them across several topics. So the critically-damped response is at the frontier between the two, mathematically and physically, and not easy distinguishable at first sight when very near to the critical value.
In fact, the under-damping case will always be evidenced by more or less visible oscillations. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.
Create a free Team What is Teams? Learn more. Difference between critically damped systems and overdamped systems Ask Question. Asked 4 years, 5 months ago. Active 3 years, 7 months ago. Viewed 2k times. Begin typing your search term above and press enter to search. Press ESC to cancel. Skip to content Home Engineering What are over damped critically and under damped systems? Ben Davis September 19, What are over damped critically and under damped systems? What is the effect of damping in an oscillatory system?
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