The formula to calculate the Rise Time is:
\[ t_r = \frac{\pi - \Phi}{\omega_d} \]
Rise Time is the time required to reach the final value by an underdamped time response signal during its first cycle of oscillation. Phase Shift is defined as the shift or difference between the angles or phases of two unique signals. Damped Natural Frequency is a particular frequency at which if a resonant mechanical structure is set in motion and left to its own devices, it will continue oscillating at a particular frequency.
Let's assume the following values:
Using the formula:
\[ t_r = \frac{\pi - 0.27}{22.88} = 0.125506671922631 \]
| Phase Shift (Φ) | Damped Natural Frequency (ωd) | Rise Time (tr) |
|---|---|---|
| 0.1 | 22.88 | 0.132936741852701 |
| 0.2 | 22.88 | 0.128566112482071 |
| 0.3 | 22.88 | 0.124195483111442 |
| 0.4 | 22.88 | 0.119824853740813 |
| 0.5 | 22.88 | 0.115454224370183 |