Allusion is made below to recent work on the production of undamped trains of electric waves.
For undamped sinusoids, the signal space can be inferred from the complex roots found with a magnitude very close to 1.0.
From this, you should be able to find the natural undamped frequency, w.
Poulsen's method of producing continuous or undamped electrical waves has been applied by him in radio-telegraphy.
The time required for an undamped system to complete one cycle of free vibration is the natural period of vibration of the system.
There are also three Undamped Algorithms for fitting sinusoids via a modification of the least-squares Prony method.
This allows routine computation of undamped vibration of any linear structure, for example by Finite Element methods.
Using this method, it is possible to fit exponentially damped sines, undamped sines, and damped exponentials.