Every object and physical system has a natural frequency - or frequencies - of vibration. For many simple systems there is an equation for this frequency.
For a pendulum,  
\[f=\frac{1}{2 \pi} \sqrt{\frac{g}{l}}\]

For a vertically oscillating spring,  
\[f=\frac{1}{2 \pi} \sqrt{\frac{k}{m}}\]

Any oscillating system can be made to oscillate at any frequency  
  resonate by applying an external stimulus 
  times per second. The frequency  
  is called the driving frequency. If the driving frequency is equal to the natural frequency, then the amplitude of the oscillation reaches a maximum, and so does the energy of the system. Many systems dissipate this energy by some mechanism - friction or air resistance. If this is not possible the the system may oscillate to destruction. The best example is the Tacoma narrow bridge - nicknamed 'Galloping Gertie', which collapsed when the driving force was applied by wind in 1940.

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