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9. (20%) As shown in figure, a force F is applied on the free end of a cantilever, where the displacement in the free end is $\delta$ following the force direction. The rigidity factor of the cantilever is defined as the ratio of force by unit displacement. The length L and its width b are measured using two different rulers. The recorded data are listed in following table 1. Table 1. The recorded length L and width b of the cantilever L(cm) 13.98 14.20 13.94 14.16 14.04 14.08 14.00 14.20 13.96 b (cm) 4.09 4.06 4.02 4.07 4.05 4.04 4.07 4.07 4.09 1) Gives the mathematic formula of the rigidity factor of this cantilever. 2) What are the mean and standard deviations of the measured length and width? 3) Suppose the thickness is What is the volume and its uncertainty of this cylinder? 4) When the dimensional tolerance of this cantilever are $\Delta L = 5\%$ L, $\Delta h = 5\%$ h, $\Delta b = 5\%$ b, what is the standard deviation and the simpler average errors of its rigidity factor? 5) Give the generally formula of its natural frequency of this cantilever as shown in figure?

          9. (20%) As shown in figure, a force F is applied on the free end of a cantilever, where the displacement in the free end is \(\delta\) following the force direction. The rigidity factor of the cantilever is defined as the ratio of force by unit displacement. The length L and its width b are measured using two different rulers. The recorded data are listed in following table 1.

Table 1. The recorded length L and width b of the cantilever
L(cm) 13.98 14.20 13.94 14.16 14.04 14.08 14.00 14.20 13.96
b (cm) 4.09 4.06 4.02 4.07 4.05 4.04 4.07 4.07 4.09

1) Gives the mathematic formula of the rigidity factor of this cantilever.
2) What are the mean and standard deviations of the measured length and width?
3) Suppose the thickness is What is the volume and its uncertainty of this cylinder?
4) When the dimensional tolerance of this cantilever are \(\Delta L = 5\%\) L, \(\Delta h = 5\%\) h, \(\Delta b = 5\%\) b, what is the standard deviation and the simpler average errors of its rigidity factor?
5) Give the generally formula of its natural frequency of this cantilever as shown in figure?

$9. (20%) As shown in figure, a force F is applied on the free end of a cantilever, where the displacement in the free end is $\delta$ following the force direction. The rigidity factor of the cantilever is defined as the ratio of force by unit displacement. The length L and its width b are measured using two different rulers. The recorded data are listed in following table 1. Table 1. The recorded length L and width b of the cantilever L(cm) 13.98 14.20 13.94 14.16 14.04 14.08 14.00 14.20 13.96 b (cm) 4.09 4.06 4.02 4.07 4.05 4.04 4.07 4.07 4.09 1) Gives the mathematic formula of the rigidity factor of this cantilever. 2) What are the mean and standard deviations of the measured length and width? 3) Suppose the thickness is What is the volume and its uncertainty of this cylinder? 4) When the dimensional tolerance of this cantilever are Δ L = 5% L, Δ h = 5% h, Δ b = 5% b, what is the standard deviation and the simpler average errors of its rigidity factor? 5) Give the generally formula of its natural frequency of this cantilever as shown in figure?$

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