What is damping ratio formula?

The damping ratio formula is defined as the ratio of the actual damping coefficient to the critical damping coefficient. It helps to measure the effectiveness of damping in a system and indicates how quickly the system returns to its equilibrium position after being displaced.

The damping ratio is denoted by the symbol ζ and can be calculated using the following formula:

ζ = c / 2 * sqrt(k * m)

Where:

• ζ is the damping ratio
• c is the actual damping coefficient
• k is the spring constant
• m is the mass of the system

The critical damping coefficient is equal to 2 * sqrt(k * m), which represents the minimum level of damping required to prevent overshooting or oscillations in the system. A damping ratio of less than 1 indicates underdamping, a value of 1 signifies critical damping, and a value greater than 1 denotes overdamping.