Resonance

Resonant frequency is a natural frequency of vibration determined by the physical parameters of the vibrating object. This same basic idea of physically determined natural frequencies applies throughout physics in mechanics, electricity and magnetism, and even throughout the realm of modern physics.

It is easy to get an object to vibrate at its resonant frequencies, hard at other frequencies. A child's playground swing is an example of a pendulum, a resonant system with only one resonant frequency. With a tiny push on the swing each time it comes back to you, you can continue to build up the amplitude of swing. If you try to force it to swing a twice that frequency, you will find it very difficult, and might even lose teeth in the process!

Swinging a child in a playground swing is an easy job because you are helped by its natural frequency.

Definition and graphic provided by hyperphysics

Mathematically Resonance is simple idea

If the position of an object in simple harmonic motion is:

Then if a force is applied to that object at the same frequency then the object is in resonance.