Natural frequency is the natural frequency of a second order delay element designed to be damping-free,
If a system capable of oscillation such as a spring-mass system is prompted to oscillate as a result of sinusoidal external excitation (usually in the form of continuous oscillation), and assuming excitation is based on the natural frequency (f = f o), the phase angle = —90o and the amplitude will be 1/2 the initial amplitude where f = 0.
With a high response proportional valve, the natural frequency for the valve should be much higher (around two to three times higher) than the natural frequency for the hydraulic actuator to ensure the system as a whole can deliver good dynamic performance.