viabracion libre con amortiguaiento

1. VIBRACION LIBRE CON AMORTIGUAMIENTO
Datos:
≔W 25.8 ≔g 981
≔k 8.36 ≔β %6.2
condiciones iniciales °
≔U 6.83
≔U' 36
formulas
≔m =―
W
g
0.03
≔ω =
‾‾‾
―
k
m
17.83
≔ωD =⋅ω ‾‾‾‾‾-1 β2
17.79
≔TD =――
⋅2 π
ωD
0.35
≔A =――――
+U' ⋅⋅β ω U
ωD
2.45
≔B =U 6.83
≔a =‾‾‾‾‾‾‾+A2
B2
7.26
≔θ =atan
⎛
⎜
⎝
―
A
B
⎞
⎟
⎠
0.34
≔t1 =――
θ
ωD
0.02
≔U1 =⋅a e ⋅-β θ
7.1
≔tf =―――
ln
⎛
⎜
⎝
――
a
0.01
⎞
⎟
⎠
⋅β ω
5.96
≔#ciclos =――
tf
TD
16.88
≔U((t)) →⋅e ⋅⋅-β ω t
⎛⎝ +⋅A sin⎛⎝ ⋅ωD t⎞⎠ ⋅B cos⎛⎝ ⋅ωD t⎞⎠⎞⎠ ⋅e ⋅-1.105400047546714558 t
(( ⋅6.83 cos(( ⋅17.79473262905444

2. U(t) e ⎝ +sin⎝ωD t⎠ cos⎝ωD t⎠⎠ e (6.83 cos(17.79473262905444
GRAFICA DE DESPLAZAMIENTOS
-3
-1.5
0
1.5
3
4.5
6
7.5
-6
-4.5
9
2 3 4 5 6 70 1
t
GRAFICA VELOCIDADES
→――
d
dt
U((t)) e...
-50
-25
0
25
50
75
100
2 3 4 5 6 70 1

3. -75
-125
-100
t
GRAFICA ACELERACIONES
→――
d
d
2
t2
U((t)) ⋅e ⋅-1.105400047546714558 t
(( -⋅-774.95851199560441694 sin(( ⋅17.79473262905444 t)) 2162.7
-1800
-1350
-900
-450
0
450
900
1350
1800
-2700
-2250
2250
2 3 4 5 6 70 1
t