# Mechanical Resonance

An oscillator is anything that vibrates or oscillates. Examples would include:

• A pendulum (think: you on a playground swing)
• A mass hanging from a spring
• A piece of material fixed at one end but free at the other end (think: a ruler held over the edge of a table, and you "twang" the free end)

Oscillators will always have a particular natural frequency, which is the reciprocal of the period of its oscillation. For a pendulum, the natural frequency will depend on its length. For a mass on a spring, it depends on the amount of mass, and how stiff the spring is.

As a concrete example, imagine yourself on a playground swing, and someone is pushing you. Let's say this person's name is Pat. Does Pat push you continuously? No, instead Pat pushes only part of the time, once per swing, only when you are moving away. Why? If Pat pushed you while you were going towards Pat, you would slow down.

{More technical explanation: Recall our definition of work, force times distance, and that work can change the kinetic energy of an object. When the force is in the same direction as the motion, the work is positive and the change in KE is positive, i.e. you speed up. When the force is opposite the direction of motion, the work is negative and so is the change in KE: you slow down.}

This is an example of mechanical resonance: if you push on an oscillator(even with only a slight force) with a frequency equal to the oscillator's natural frequency, the amplitude of the motion will increase.

Activities & Practice