The formula to calculate the Bandwidth Frequency is:
\[ f_b = \omega_n \left( \sqrt{1 - (2 \zeta^2)} + \sqrt{\zeta^4 - (4 \zeta^2) + 2} \right) \]
Bandwidth Frequency is the range of frequencies over which the magnitude of the frequency domain drops to 70.7% from its zero frequency value. Natural Frequency of Oscillation refers to the frequency at which a physical system or structure will oscillate or vibrate when it is disturbed from its equilibrium position. Damping Ratio in a control system is defined as the ratio with which any signal gets decayed.
Let's assume the following values:
Using the formula:
\[ f_b = 23 \left( \sqrt{1 - (2 \cdot 0.1^2)} + \sqrt{0.1^4 - (4 \cdot 0.1^2) + 2} \right) = 54.9696597723011 \]
| Natural Frequency (ωn) | Damping Ratio (ζ) | Bandwidth Frequency (fb) |
|---|---|---|
| 20 | 0.1 | 47.799704149827065 |
| 21 | 0.1 | 50.189689357318414 |
| 22 | 0.1 | 52.579674564809771 |
| 23 | 0.1 | 54.969659772301128 |
| 24 | 0.1 | 57.359644979792478 |
| 25 | 0.1 | 59.749630187283827 |