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20 Φεβ 2013 · Damping removes energy from the system and so the amplitude of the oscillations goes to zero over time, regardless of the amount of damping. However, the system can have three qualitatively different behaviors: under-damping, critical damping, and over-damping.
This review summarizes the basic principles of vibration control and analyses the vibration control strategies for different damping materials and damping structures. Meanwhile, various models of bio-damped structures are outlined.
Under, Over and Critical Damping OCW 18.03SC.. . Example 3. Show that the system x + 4x + 4x = 0 is critically damped and . graph the solution with initial conditions x(0) = 1, x(0) = 0. Solution. Characteristic equation: s2 +4s + 4 = 0. Characteristic roots: (this factors) −2, −2. Exponential solutions: (only one) e−2t. General solution:
Critical damping viewed as the minimum value of damping that prevents oscillation is a desirable solution to many vibration problems. Increased damping implies more energy dissipation, and more phase lag in the response of a system. Reduced damping means more oscillation, which is often undesirable.
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.
27 Μαΐ 2024 · Figure 13.5: Examples of underdamped, overdamped and critically damped free vibrations. For overdamped and critically damped vibrations, different initial conditions are shown for the same ratio \(c / m_{A}\).
