The formula to calculate the Resonant Peak is:
\[ M_r = \frac{1}{2 \cdot \zeta \cdot \sqrt{1 - \zeta^2}} \]
Resonant Peak is the peak (maximum) value of the magnitude of the frequency domain. It is denoted by Mr. Damping Ratio in a control system is defined as the ratio with which any signal gets decayed.
Let's assume the following value:
Using the formula:
\[ M_r = \frac{1}{2 \cdot 0.1 \cdot \sqrt{1 - 0.1^2}} = 5.02518907629606 \]
| Damping Ratio (ζ) | Resonant Peak (Mr) |
|---|---|
| 0.05 | 10.012523486435176 |
| 0.06 | 8.348373955217301 |
| 0.07 | 7.160421719097442 |
| 0.08 | 6.270096514883813 |
| 0.09 | 5.578193172283424 |
| 0.1 | 5.025189076296061 |
| 0.11 | 4.573206651312431 |
| 0.12 | 4.196994604298856 |
| 0.13 | 3.879071672221347 |
| 0.14 | 3.606951621637397 |
| 0.15 | 3.371478249494491 |