To design stiffness (k) and damping coefficient (c) for a system with the given requirements, we need to consider the desired amplitude and the preference for under-damped behavior. The damping ratio (ζ) is a key parameter that determines the behavior of the system's response.
In an under-damped system, the damping ratio (ζ) should be between 0 and 1. If ζ = 0, the system is undamped, while ζ = 1 represents critical damping. As the damping ratio increases beyond 1, the system becomes over-damped.
Since under-damped behavior is preferred, we can focus on damping ratios below 1. However, the specific range for the damping ratio would depend on the desired amplitude constraint of less than 0.145.
To determine the best range for the damping ratio, we need more information about the system and its characteristics, such as the natural frequency, the equation of motion, or any other constraints provided in the project. The relationship between the damping ratio, natural frequency, and amplitude of the system's response is important in determining the appropriate range for ζ.
Once we have additional information, we can perform calculations or simulations to analyze the system's response and find a suitable range for the damping ratio that satisfies the given amplitude constraint while maintaining under-damped behavior.
It's worth mentioning that there is usually a trade-off between the damping ratio and the amplitude of the system's response. Higher damping ratios tend to reduce the amplitude faster, but they may also introduce higher energy dissipation in the system. Therefore, finding the best range for the damping ratio requires careful consideration of the specific system requirements and design constraints.