Resonance

As the dampening increases, the period and frequency will begin to be affected so that the object moves toward equilibrium. In some cases, such as with a car suspension, the goal is to dampen them as quickly as possible. This leads to a critical dampening, which is defined as the condition in which there is dampening to the maximal degree as quickly as possible. The goal is not to underdamp the system or overdamp the system.

An underdamped system will oscillate through the equilibrium position and an overdamped system will move more slowly toward equilibrium than one that is critically damped. Critical damping will return the system to equilibrium as quickly as possible without overshooting.

RESONANCE

All objects will have a resonance frequency. This is the natural frequency of the object when a periodic force is applied to it. The driving force will put energy into a system but will not put energy into a system necessarily at the resonance frequency of the object. The natural frequency of an object is the frequency it would oscillate if there were no driving force and no damping force. If you drive or force a system at its resonance frequency, the amplitude will naturally increase. This phenomenon is called resonance.

This is why it takes a certain frequency to break a glass. The frequency of a certain sound will reach the resonant frequency of the glass so that the glass vibrates and increases in amplitude, with the amplitude being so great eventually that it breaks the glass. Heavy damping will reduce the amplitude; the less damping at the resonant frequency will narrow the resonance frequency. Little damping is necessary for musical instruments like pianos, while automobile suspension systems will require heavy damping, which will reduce the amplitude.

When one tunes a radio, the resonant frequency is being adjusted so that the radio oscillates only at the station’s broadcast frequency. Magnetic resonance imaging used in medicine involves resonating hydrogen nuclei using incoming radio waves. Swinging a child on a swing involves pushing at the natural resonant frequency of the swing to achieve maximum amplitude. The efficiency of energy transfer from the driving force into the oscillator is best at the resonant frequency.