The natural frequency increases with increases in stiffness and decreases with increases in mass. When a driving system imposes a particular frequency on the driven system, then it is called the forced vibration . This is analogous to you walking or running with the swing back and forth. In this case you determine the rate of oscillation of the swing. The opposition to displacement or movement is called impedance .
Resistance is independent of frequency and is the cause of damping in free vibration.
In a vibrating system, at a certain frequency or frequencies, the mass and compliance reactance are equal and cancel each other out resulting in the most efficient transfer of energy and the largest amplitude of vibration for the given amount of force applied. The reactance is at its minimum at the system's natural frequency. When a driving system, whose natural frequency is identical or similar to the natural frequency of the driven system, causes the driven system to vibrate at its natural frequency or frequencies, the amplitude of oscillation will be the largest for a given amount of force applied to driven system. This is known as resonance . The natural frequency is also known as the resonant frequency .