The formula to calculate the Critical Damping Ratio is:
\[ \zeta = \frac{c}{2 \sqrt{m \cdot k}} \]
Where:
The critical damping ratio is a dimensionless measure of damping in a system relative to critical damping. It indicates how oscillations in a system decay after a disturbance. A system is critically damped when the damping ratio is equal to 1, meaning it returns to equilibrium as quickly as possible without oscillating. If the damping ratio is less than 1, the system is underdamped and will oscillate. If the damping ratio is greater than 1, the system is overdamped and will return to equilibrium slowly without oscillating.
Let's assume the following values:
Using the formula to calculate the Critical Damping Ratio:
\[ \zeta = \frac{10}{2 \sqrt{2 \cdot 50}} = \frac{10}{2 \sqrt{100}} = \frac{10}{20} = 0.5 \]
The Critical Damping Ratio is 0.5, indicating an underdamped system.
