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Physics, 21.10.2020 16:01 raywils0n12300p0t3yc
Under the assumption that the beam is a rectangular cantilever beam that is free to vibrate, the theoretical first natural frequency of the beam in terms of the length, L, width, b, thickness, h, density, p, and Young's Modulus, E, in Hertz is given by:
fn= h/2πL^2 √E/rho
The density of steel used in the beam is 7800 kg/m^3, and its Young's Modulus is 210 GPa. You measure the dimensions of the clamped steel beam with a set of calipers and gather the following data:
L = 233.5 mm, b = 24.9 mm, h = 3.3 mm
The calipers used to measure the dimensions of beam have a resolution of 0.01 mm and therefore have an uncertainty of +0.005 mm.
Required:
a. What is the uncertainty of the natural frequency (in Hz) due to the uncertainty of the length measurement?
b. What is the uncertainty of the natural frequency (in Hz) due to the uncertainty of the width measurement?
c. What is the uncertainty of the natural frequency (in Hz) due to the uncertainty of the thickness measurement?
d. What is the total uncertainty of the natural frequency due to the beam measurements (in Hz)?
e. What is the theoretical first natural frequency of the beam including the measurement uncertainty?
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