```python
from sympy.physics.mechanics import *
import sympy as sp
mechanics_printing(pretty_print=True)
```


```python
m, l, l01, l02, k1, k2 = sp.symbols(r'm l l_{0\,1} l_{0\,2} k_1 k_2')
t, g, h, w = sp.symbols('t g h w')
v = dynamicsymbols(r'\theta')
dv = dynamicsymbols(r'\theta', 1)
```


```python
x = l * sp.sin(v)
y = -l * sp.cos(v)

dx = x.diff(t)
dy = y.diff(t)
```


```python
V = m*g*y + sp.Rational(1,2)*k1*(sp.sqrt((x+w)**2+(y+l)**2)-l01)**2+sp.Rational(1,2)*k2*(sp.sqrt((x-w)**2+(y+l)**2)-l02)**2
T = sp.Rational(1,2)*m*(dx**2+dy**2)
L = T - V
```


```python
LM = LagrangesMethod(L, [v])
```


```python
soln = LM.form_lagranges_equations()
```


```python
solvedsoln = sp.solve(sp.Eq(soln[0]), v.diff(t,t))
```


```python
solvedsoln
```


```python
sp.latex(solvedsoln)
```




    '\\left [ \\frac{- g m \\sin{\\left (\\theta{\\left (t \\right )} \\right )} + \\frac{k_{1} l l_{0,1} \\sin{\\left (\\theta{\\left (t \\right )} \\right )}}{\\sqrt{- 2 l^{2} \\cos{\\left (\\theta{\\left (t \\right )} \\right )} + 2 l^{2} + 2 l w \\sin{\\left (\\theta{\\left (t \\right )} \\right )} + w^{2}}} - k_{1} l \\sin{\\left (\\theta{\\left (t \\right )} \\right )} + \\frac{k_{1} l_{0,1} w \\cos{\\left (\\theta{\\left (t \\right )} \\right )}}{\\sqrt{- 2 l^{2} \\cos{\\left (\\theta{\\left (t \\right )} \\right )} + 2 l^{2} + 2 l w \\sin{\\left (\\theta{\\left (t \\right )} \\right )} + w^{2}}} - k_{1} w \\cos{\\left (\\theta{\\left (t \\right )} \\right )} + \\frac{k_{2} l l_{0,2} \\sin{\\left (\\theta{\\left (t \\right )} \\right )}}{\\sqrt{- 2 l^{2} \\cos{\\left (\\theta{\\left (t \\right )} \\right )} + 2 l^{2} - 2 l w \\sin{\\left (\\theta{\\left (t \\right )} \\right )} + w^{2}}} - k_{2} l \\sin{\\left (\\theta{\\left (t \\right )} \\right )} - \\frac{k_{2} l_{0,2} w \\cos{\\left (\\theta{\\left (t \\right )} \\right )}}{\\sqrt{- 2 l^{2} \\cos{\\left (\\theta{\\left (t \\right )} \\right )} + 2 l^{2} - 2 l w \\sin{\\left (\\theta{\\left (t \\right )} \\right )} + w^{2}}} + k_{2} w \\cos{\\left (\\theta{\\left (t \\right )} \\right )}}{l m}\\right ]'




```python

```

4435a4743db05dcc1124a286e8910a9487502535
ipynb
Jupyter Notebook
Pendula/Misc/SpringLoadedPendulum/SpringLoadedPendulum.ipynb
ethank5149/Classical-Mechanics
4684cc91abcf65a684237c6ec21246d5cebd232a
MIT
Pendula/Misc/SpringLoadedPendulum/SpringLoadedPendulum.ipynb
ethank5149/Classical-Mechanics
4684cc91abcf65a684237c6ec21246d5cebd232a
MIT
Pendula/Misc/SpringLoadedPendulum/SpringLoadedPendulum.ipynb
ethank5149/Classical-Mechanics
4684cc91abcf65a684237c6ec21246d5cebd232a
MIT
Qwen/Qwen-72B
1. YES
2. YES