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

Table 3

Comparison of approximate and “Exact” frequencies for Case  3.

Constant parameters						Approximate solutions		Exact solution	|𝜔−𝜔ex|/𝜔ex
𝑚1	𝑚2	𝑘1	𝑘2	𝑋0	𝑌0	𝜔1	𝜔2	𝜔ex	𝜔=𝜔1	𝜔=𝜔2
1	2	5	1	−4	1	5.9687	5.8885	5.8892	1.35%	0.011%
3	5	2	5	5	−5	14.1798	13.8710	13.8752	2.20%	0.011%
1	5	5	1	5	−5	9.7980	9.6096	9.6119	1.94%	0.023%
10	5	10	10	20	30	15.0997	14.7763	14.7806	2.16%	0.029%
5	10	50	−0.01	−20	40	2.6268	2.5452	2.5468	3.14%	0.064%
100	1	10	5	20	25	10.2366	10.0545	10.0564	1.79%	0.020%
50	100	50	100	100	25	112.5067	110.0293	110.0633	2.22%	0.031%
1000	100	200	300	400	200	314.6461	307.7164	307.8115	2.17%	0.031%