Resonance and natural frequency

[Theroen]

Homework Statement

Ok, this is not homework, just something that's been bugging me and my tutor is unavailable(as usual) to help me. Why does increasing the mass of a system lower its natural frequency, like adding a concrete block to a washing machine. Come to think of it, I'm not even too sure about what natural frequency is. I know that it's the frequency at which resonance occurs, if the driving frequency is equal to the natural frequency, but what determines the natural frequency? How to obtain it?

The Attempt at a Solution

I figured out that adding a concrete block is not damping, since it becomes a part of the system in oscillation, and not an external resistive force. Therefore the addition of the block does not damp the oscillation, but it changes the system's natural frequency, but then I come back to the problem of how additional mass affects natural frequency.

 

[Unto]

Every object has a natural frequency which is the way it vibrates without having any external forces acting upon it. If you apply an external force to this object, it will vibrate, but maybe not at it's natural frequency. However is the driving force is more or less equal to the natural frequency, resonance will occur.

Adding a mass to an object alters it's natural frequency - it shouldn't be hard to see why. In large cases such a bridges, adding blocks to it changes it's natural frequency, so it would be more difficult for wind to resonate it given that wind provides a more or less constant driving force.

This is generally called damping a system. The same effect can also happen by making the system lighter - to the end of disrupting the driving forces ability to resonate the system.

Basically remember these 3 instances:

f >> f0 (minimal movement or a very low frequency induced)
f << f0 (system is moved, but very slowly. It may however gain amplitude or increased frequency over time)
f = f0 (ocsilations become large and destructive, this is resonance)

Where f = natural frequency
f0 = driving frequency/force.