Project #1 ME-130

	A	B	C	D	E	F	G	H	I	J	K	L	M	O
1		Inputs: ONLY CHANGE HERE		Auxiliary Root	Case:		General Equation X(t)							#ERROR!
2	m (N)	1.6		74973.6	Underdamped		X(t) =	C1(e^-0.058t) + C2(e^-171.192t) + 0.0625 Cos(0t) + 0 Sin(0t)
3	β (N s/m)	274					Full Solution X(t) and X'(t) (Solved C1 and C2)
4	k (N/m)	16		Natural Frequency (ω*)	Frequency Overlap?		X(t) =	0.9495 (e^-0.058t) + -0.012 (e^-171.192t) + 0.0625 Cos(0t) + 0 Sin(0t)
5	x(0) (m)	1		85.56658591	False		X'(t) =	-0.0551e^(-0.058t) + 2.0543e^(-171.192t) - 0 Sin(0t) + 0 Cos(0t)
6	x'(0) (m/s)	2			^ if ωo=ω*
7	Fo	1		M1 =	-0.058	N/A	= α		Amplitude 'A'
8	ωo	0		M2 =	-171.192	N/A	= β		0.9495803645
9	Range of t (s)	500		Characteristic Eqn =	1.6 λ^2 + 274 λ + 16
10		^ affects the graphing 0 < t < x
11	Particular Soln Matrix (Constants A and B)					C1 and C2 Soln Matrix					X(t) (m)	X'(t) (m/s)	time t (second)
12	16.000000000000000000000000000000	0.000000000000000000000000000000	A	1		1.000000000000000000000000000000	1.000000000000000000000000000000	C1	0.9375		1.000000	1.999233	0
13	0.000000000000000000000000000000	16.000000000000000000000000000000	B	0		-0.058000000000000000000000000000	-171.192000000000000000000000000000	C2	2		0.522366	-0.026672	12.5
14	Inverse Multiplication					Inverse Multiplication					0.285224	-0.012918	25
15	0.062500000000000000000000000000	0.000000000000000000000000000000	1	0.062500000000000000000000000000	0.0625	1.000338915703480000000000000000	0.005843374197996890000000000000	0.9375	0.949504481868010000000000000000	0.9495	0.170371	-0.006257	37.5
16	0.000000000000000000000000000000	0.062500000000000000000000000000	0	0.000000000000000000000000000000	0.0000	-0.000338915703483820000000000000	-0.005843374197996890000000000000	2	-0.012004481868009900000000000000	-0.0120	0.114745	-0.003030	50
17											0.087803	-0.001468	62.5
18	Xp =	0.0625 Cos(0t) + 0 Sin(0t)									0.074755	-0.000711	75
19	Xh =	C1(e^-0.058t) + C2(e^-171.192t)									0.068435	-0.000344	87.5
20	Xh (final)=	0.9495 (e^-0.058t) + -0.012 (e^-171.192t)									0.065375	-0.000167	100
21											0.063892	-0.000081	112.5
22	Notes:										0.063174	-0.000039	125
23	3 Damped cases of motion:		2 cases Undamped:								0.062827	-0.000019	137.5
24	-Unique roots		- Imaginary where, ωo=ω*								0.062658	-0.000009	150
25	-Identical Roots		- Normal imaginary roots (ωo does NOT equal ω*)								0.062577	-0.000004	162.5
26	-Imaginary roots										0.062537	-0.000002	175
27											0.062518	-0.000001	187.5
28	Imaginary Roots of damped case is the same solution form as Normal imaginary Undamped Roots										0.062509	-0.000001	200
29	Therefore, we effectively have 4 TRUE cases in terms of forms of solutions										0.062504	0.000000	212.5
30											0.062502	0.000000	225
31											0.062501	0.000000	237.5
32											0.062500	0.000000	250
33											0.062500	0.000000	262.5
34	CASE SOLUTION DISPLAY DATABASE: (DO NOT MODIFY)										0.062500	0.000000	275
35	Case 1	-0.0551e^(-0.058t) + 2.0543e^(-171.192t) - 0 Sin(0t) + 0 Cos(0t)									0.062500	0.000000	287.5
36	Case 2	-0.0551e^(-0.058t) + 2.0543te^(-171.192t) + -0.0120044818680099e^(-171.192t) - 0 Sin(0t) + 0 Cos(0t)									0.062500	0.000000	300
37	Case 3	#VALUE!									0.062500	0.000000	312.5
38	Case4	#VALUE!									0.062500	0.000000	325
39											0.062500	0.000000	337.5
40											0.062500	0.000000	350
41											0.062500	0.000000	362.5
42											0.062500	0.000000	375
43											0.062500	0.000000	387.5
44											0.062500	0.000000	400
45											0.062500	0.000000	412.5
46											0.062500	0.000000	425
47											0.062500	0.000000	437.5
48											0.062500	0.000000	450
49											0.062500	0.000000	462.5
50											0.062500	0.000000	475
51											0.062500	0.000000	487.5
52											0.062500	0.000000	500
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