Discussion of the Improved Methods for Analyzing a Cantilever Beam Carrying a Tip-Mass under Base Excitation

Table 3

The first natural frequencies and the resonant displacements at some certain positions.

Resonant frequency or positions	The values of frequencies and displacement responses (Hz or mm)			Errors
	Theory based on 𝑈1^(2)(𝑥)	Theory based on 𝑈1^(3)(𝑥)	Experiment
The 1st natural frequency	81.5	81.5	81.2	0.37%
𝑥 = 36.4 mm	0.1285	0.1285	0.1277	0.62%
𝑥 = 57.4 mm	0.3022	0.3022	0.3001	0.69%
𝑥 = 78.4 mm	0.5279	0.5279	0.5246	0.63%
𝑥 = 99.4 mm	0.7905	0.7905	0.7855	0.63%
𝑥 = 120.4 mm	1.0742	1.0742	1.0671	0.66%