## Earthquakes in the laboratory

Practical Activity for 14-16

**Demonstration**

Buildings in earthquake zones need to be designed with modes of vibration and resonance in mind.

Apparatus and Materials

- Signal generator
- Vibration generator
- Leads
- Materials for building tower (e.g. drinking straws, spaghetti, K'nex, sticky tape, blu-tack, glue gun)
- Forcemeter, reading up to 10 N
- Ruler
- Electronic balance
- Earthquake table

Health & Safety and Technical Notes

Hammerite paints use xylene as the solvent. When painting just one earthquake table, work in a well-ventilated area, e.g. close to an open window. If more than one table is painted on the same day, work out-of-doors.

Read our standard health & safety guidance

For construction details of the earthquake table see apparatus entry.

Procedure

- Students design and build their own tower structures for testing, preferably tall and flimsy. Mount the tower on the earthquake table.
- Set the signal generator at a low frequency (a few Hz) and observe the resulting vibrations of the tower as the frequency is gradually increased.

Teaching Notes

- Points you could discuss:
- Qualitatively, the phenomenon of resonance: at certain distinct frequencies, vibrations build up to a large amplitude.
- Modes of vibration: at one frequency all parts of the tower move in phase (all in the same direction at the same time) and at other frequencies some parts move in one direction while other parts move in the opposite direction.
- In an earthquake zone, it is important to design tall buildings in such a way as to
avoid

resonance. The frequencies that make the structure resonate must not be the same as typical frequencies of earthquake waves. - Students may then explore factors affecting the resonant frequencies of their structures.
- They could also use a simple mathematical model to predict the lowest resonant frequency of their tower, and compare this with the measured frequency.
- A vibrating tower of mass
*m*, height*h*andstiffness

*k*can be modelled, mathematically, as a single mass*m*mounted at a height*h*above the base on a massless support ofstiffness

*k*. The structure resonates at frequency*f = 1/T*where*T*= 2π*√(k/m)* - The stiffness of the tower can be measured by attaching a forcemeter at height of about 2
*h*/3 above the base and measuring the force,*F*, needed to produce a horizontal displacement*x*. Then*k = F/x*.

This experiment comes from University of York Science Education Group:

Salters Horners Advanced Physics©

*Diagrams are reproduced by permission of the copyright holders, Heinemann.*

*This experiment was safety-tested in April 2006*