```python
 from sympy import *
init_printing()
```


```python
x = Symbol('x')
EI = Symbol('EI')
R = Symbol('R')
omega = Symbol('omega')
ll = Symbol('lambda')
```


```python
gamma_1 = x
```


```python
gamma_2 = 10*x**3/3 - 10*x**4/3 + x**5
```


```python
A11 = integrate(gamma_1*gamma_1, (x, 0, 1))
```


```python
A12 = integrate(gamma_1*gamma_2, (x, 0, 1))
```


```python
A12
```


```python
A22 = integrate(gamma_2*gamma_2, (x, 0, 1))
```


```python
G = integrate(omega**2*x, (x,x*R, R))
```


```python
G
```


```python
def calcB(gamma_1, gamma_2):
    der1_2 = diff(gamma_1,x,2)
    der1_1 = diff(gamma_1,x,1)
    der2_1 = diff(gamma_2,x,1)
    integrando = EI*der1_2*der2_2+R**2*G*der1_1*der2_1
    sol = integrate(integrando,(x, 0, 1))/(2*R)/(omega**2*R**3)
    return(sol*2)
```


```python
B11 = calcB(gamma_1, gamma_1)
```


```python
B12 = calcB(gamma_1, gamma_2)
```


```python
B22 = calcB(gamma_2, gamma_2).simplify()
```


```python
k = Symbol('k')
```


```python
B22 = B22.subs(EI,k*R**4*omega**2)
```


```python
B22
```


```python
LHS =  Matrix([[B11, B12], [B12, B22]])- ll**2*Matrix([[A11, A12], [A12, A22]])
```


```python
LHS
```


```python
determinante = det(LHS).subs(k,0.004).simplify()
```


```python
factor(determinante)
```


```python
soluciones = roots(determinante)
```


```python
sol = list(soluciones.keys());
```


```python
sol
```


```python
phi_1 = Symbol('phi_1')
phi_2 = Symbol('phi_2')
```


```python
Sistema = LHS.subs(k,0.004).subs(ll, sol[2])
Sistema = Sistema.col_insert(2, Matrix([0, 0]))
solve_linear_system(Sistema, phi_1, phi_2)
Sistema
```


```python
Modo1 = gamma_1
```


```python
Sistema = LHS.subs(k,0.004).subs(ll, sol[3])
Sistema = Sistema.col_insert(2, Matrix([0, 0]))
solve_linear_system(Sistema, phi_1, phi_2)
```


```python
Modo2 = -0.76*gamma_1+gamma_2
Modo2 = Modo2/Modo2.subs(x,1.0)
```


```python
Modo2
```


```python
p1 = plot(Modo2,Modo1,(x, 0, 1))
```


```python

```

f85a929117ebad50e263a96fad769e3d3148e559
ipynb
Jupyter Notebook
Vibraciones.ipynb
garcgutierrez/DAS
a557bc69e486559c7ed784f8c0c4dffdd9180749
Apache-2.0
Vibraciones.ipynb
garcgutierrez/DAS
a557bc69e486559c7ed784f8c0c4dffdd9180749
Apache-2.0
Vibraciones.ipynb
garcgutierrez/DAS
a557bc69e486559c7ed784f8c0c4dffdd9180749
Apache-2.0
Qwen/Qwen-72B
1. YES
2. YES