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Figure 2: The free vibration response of a cantilever beam
Figure 2 shows a typical free vibration response for a carbon fibre composite beam with 100g attached at its free end.
The vibration frequency here is approximately 3.5 Hz:
Ten vibrations between 1.9s and 4.75s (2.85s)
So period T = 2.85/10 = 0.285s
Frequency (given by 1/T) = 3.5 Hz.
Figure 3: Relationship between mass and free vibration response
Figure 3 shows the typical inverse relationship between the mass attached to the free end of the beam and the free vibration response of the beam. Depending on the stiffness of the beam that you use, the curve as shown in Figure 3 can move either up or down. The inverse relationship, however, remains the same.
- Question: How does the stiffness affect the free vibration frequency?
- Answer: The stiffer the beam, the higher the vibrating frequency for a given end mass.
Teacher's notes
Safety issues:
For safety reasons it is best to ensure that the students do not look directly into the LED when it is illuminated.
Ensure the students are supervised when using the soldering iron to build the circuitry.
Time:
The expected length of the experiment including set-up time is approximately 2 hours: 1 hour for set-up and 1 hour for experiment.
Target age groups:
Ages 16+
National curriculum:
Science Key Stages: 5+
This activity would find uses in both AS/A, AVCE and degree courses. It could form the basis of an instrumentation design task or an investigation.
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