Damped angular frequency¶
A damped oscillator performs oscillations with a frequency proportional to that of an undamped oscillator, i.e. to the frequency of an oscillator when there is no damping force acting on the system.
Notes:
In the case of overdamping when the damping ratio is greater than 1, the value of damped angular frequency becomes imaginary, which indicates the absence of oscillations.
- damped_angular_frequency¶
angular_frequencyof a damped oscillator.- Symbol:
w_d- Latex:
\(\omega_\text{d}\)
- Dimension:
angle/time
- undamped_angular_frequency¶
angular_frequencyof an undamped oscillator.- Symbol:
w- Latex:
\(\omega\)
- Dimension:
angle/time
- damping_ratio¶
damping_ratioof the oscillator.- Symbol:
zeta- Latex:
\(\zeta\)
- Dimension:
dimensionless
- law¶
w_d = w * sqrt(1 - zeta^2)- Latex:
- \[\omega_\text{d} = \omega \sqrt{1 - \zeta^{2}}\]