Higher-Order Solutions of Coupled Systems Using the Parameter Expansion Method

Table 2

Comparison of approximate and “Exact” frequencies for Case  2.

Constant parameters						Approximate solutions		Exact solution	|𝜔−𝜔ex|/𝜔ex
𝑚	𝑘1	𝑘2	𝑘3	𝑋0	𝑌0	𝜔1	𝜔2	𝜔ex	𝜔=𝜔1	𝜔=𝜔2
1	1	1	1	5	1	5.1962	5.1068	5.1078	1.73%	0.0185%
2	1	3	5	8	10	4.3012	4.2401	4.2406	1.43%	0.0185%
5	10	20	30	−10	10	60.08328	58.7677	58.7856	2.21%	0.0305%
10	50	70	90	20	−40	220.4972	215.6448	215.7113	2.22%	0.0308%
10	25	20	0.5	−10	10	6.0415	5.9533	5.9541	1.47%	0.0132%
100	200	300	400	−50	50	244.9653	239.5715	239.6455	2.22%	0.0309%