# Mechanical resonance

#### dr pepper

##### Full Member level 6
If a metal plate has a resonant frequency of 100hz when struck by an object (creating an impulse) it rings at 100hz.
If the plate was subjected to a 99hz vibration would it ring at 99hz at a lesser amplitude or its resonant 100hz, assuming the Q of the plate was failry wide.
Looking at an old fashoned frequency meter that uses tuning forks I'd say the former.

#### KlausST

##### Super Moderator
Staff member
Hi,

It will move with the excitation frequency.

Klaus

#### dr pepper

##### Full Member level 6
Proving my suspicion, thanks.

#### FvM

##### Super Moderator
Staff member
It will move with the excitation frequency.
In steady state, yes. Transient response is more complex.

#### c_mitra

If a metal plate has a resonant frequency of 100hz when struck by an object (creating an impulse) it rings at 100hz.
If the plate was subjected to a 99hz vibration would it ring at 99hz at a lesser amplitude or its resonant 100hz, assuming the Q of the plate was failry wide.
1. If the object is subjected to an external periodic force with a frequency f, the object will move with the external frequency. This is called the forced vibration.

2. Now you sweep the frequency: as the external frequency (f) approaches the natural frequency (resonant frequency) we see a change in phase and amplitude but it always moves at the external frequency.

3. In spectroscopy, these are called absorption and dispersion spectrum of the object.

4. When struck by an impulse (a large force of short duration), the initial behavior is complex but after some time the object vibrates at its natural (resonant) frequency.

5. An impulse can be decomposed into a large number of frequencies with different amplitudes. However, energy from the natural frequency is absorbed strongly.

6. Electrical circuits containing reactance also show similar behavior.

#### dr pepper

##### Full Member level 6
Ok thanks for that.
Interesting on the phase change.

#### c_mitra

Ok thanks for that.
Interesting on the phase change.
Right, phase changes close to the resonance can be messy to explain.

1. Far from resonant frequency, the energy absorbed is small and the phase change is small.
2. As it approaches the resonant frequency, amplitude increases and the phase difference increases.
3. At some point close to the resonant frequency, the phase difference becomes max (positive or negative) but the amplitude continues to increase.
4. At the resonant frequency the amplitude peaks and the phase change becomes zero.
5. After the peak, the phase difference crosses to the other side (+ve to -ve or vice-versa).

The dispersion spectrum has two peaks on opposite sides and is zero at the point corresponding to the peak in the absorption spectrum.

Optical rotation in molecular spectroscopy is related to the phase difference between two circularly polarized light.

Quadrature detection in electronics is also related.