A cantilever beam with length L=200 mm, width b=12 mm and thickness t=2 mm weighs 38 grams and has a natural vibration frequency of f=42 hertz. What is the modulus of the material of the beam? You will find equations for natural frequencies of vibration and moments of area in Appendix B, Tables B12 and B2.

Data From Appendix B Table B12

Data From Table B2

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O C Beams and tubes El 3.52 f = 2 mo L4 9.87 mo P Natural frequency (s) pA Mass/length (kg/m) Density (kg/m) A = Section area (m) 22.4 2R 9.87 See Table B2 With A = 2 RI 1=R With A-Lt 2.68 L = Length of tube 2R C Disks C 1.44 2 -2R Et3 m R4 (1-2) pt Mass/area (kg/m) Thickness (m) My t 2.94 R Radius (m) Poisson's ratio FIGURE B.12 Vibrating beams, tubes and disks.