# Resonance in a vibrating body

1. Mar 16, 2014

### tennispro1213

So we're studying resonance.

It says that it occurs when an external periodic force acting on a body is exactly equal to the natural frequency of the body. The body then begins to vibrate with greater/increasing amplitude and intensity.

And so what I want to know is that is there a difference between the type of resonance that occurs in a vacuum and the type in a medium (say water) ?

Like in a vacuum, would a pendulum experiencing resonance continue to complete oscillations, or would it spin all the way around or something?

2. Mar 16, 2014

### HomogenousCow

A vacuum simply implies no air friction, resonance occurs with or without a vacuum.
Resonance occurs because the driving force is in sync with the natural vibration of the object.
In simpler terms, the driving force always pushes in the direction of vibration, never against it, thus it allows the maximum increase in amplitude.
The driving force could be from anything, a person, a machine..

3. Mar 16, 2014

### tiny-tim

hi tennispro1213! welcome to pf!
a pendulum is governed by mx'' = -mgsinθ

or approximately x'' = - (g/L)x

if you put the pendulum in a fluid, the buoyancy will change the RHS, and therefore change the resonant frequency

4. Apr 12, 2014

### tennispro1213

Ok, thanks for the answers guys.

I was just confused whether there is a difference in the increased amplitude produced due to resonance in different media.
I actually didn't clarify enough, sorry (First time using a forum (obviously)).
So what I'm asking is, would there be a greater increase in the amplitude of a body if resonance occurred in a vacuum, or would it be the same amount of increase in amplitude if resonance occurred in any medium?

(My reference to the pendulum was just an example, though thanks, that probably would have been my next question.)

5. Apr 12, 2014

### nasu

The damping produced by the medium will indeed reduce the resonant amplitude. And will make the resonance peak less sharp.

See the graph here, for example:

http://en.wikipedia.org/wiki/Resonance

Last edited: Apr 12, 2014