Dunkerley formula experiment

[no183]

ok, i have just conducted a experiment regarding dunkerley formula, after that, for sure i need a report. in the report there is the use of this equation (1/f)^2=(1/f1)^2+(1/f2)^2 where f1 f2 is natural frequency of beam and lump mass(this in experiment is the motor unit which hang at center of beam) now the questions come
1) what is the condition for resonance to occur?
2) is the support for the beam make any change to the experiment? E.G simply support, pin support etc, do it have influence?
2nd experiment, continue form the first 1, then i apply a cantilever unit with 2 mass with each at a side, after that i found the distance from center for this mass on the cantilever unit using theory, then verify it via experiment, now what i can comment about this value
theoritical value is 3.15 in while experiment value is 3.35 in. and what role does cantilever unit play for?
diagram is like this
experiment 1
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++++
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mmmm
mmmm
experiment 2
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CUCUCU
CUCUCU
cantilever unit

--mm----------mm--
--mm----------mm--
m=mass
+=motor unit
CU=cantilever unit

*note picture not to scale both mass and motor and cantilever unit at center of beam
thanks for reply..

 

[Valkarie]

1) For resonance to occur, the frequency of vibration of the beam must match the natural frequency of the motor unit. This is known as resonance frequency. 2) The support for the beam can affect the experiment results. Depending on the type of support, it can either dampen or amplify the vibrations of the beam and hence affect the resonance frequency. For the second experiment, you can comment that the theoretical value of the distance from center of the two masses on the cantilever unit matches the experimental value, with a relatively small difference. The cantilever unit serves to hold the two masses in place and to ensure that they vibrate together as one unit.