<jupyter_start><jupyter_text>Ligger op 2 stp  Berekening natuurlijke frequentie<jupyter_code>[g_k, q_k] = [4.71, 1.85]
psi2 = 0.3

q = g_k + psi2 * q_k # [kN/m1]
L = 5 # [m]
mu = q * 10**3 / 9.81
m_mod = 0.5 * mu * L
mu, m_mod
E = 10000 * 10**6 # [N/m2]
I_y = (1/12 * 1000 * 160**3) / 10**12 # [m4]
f = 2/math.pi * (3 * E * I_y / (0.49 * mu * L**4) )**0.5
E, I_y, f
from IPython.display import Markdown as md

outp = """
$\\begin{align*}
&g_{k} & &= %.2f \ kN/m^{1}  & q_{k} &= %.2f \ kN/m^{1} \\\\
&\psi_{2} & &= %.1f & l_{ov} &= %.2f m \\\\
&q_{E} & &= (g_{k} + \psi_{2} \cdot q_{k}) & &= %.1f \ kN/m^{1} \\\\
\\\\
&\mu & &= q \cdot g^{-1} & &= %.0f \ kg/m^{1} \\\\
&m_{mod} &&= 0.5 \cdot \mu \cdot \ l_{ov} & &= %.0f \ kg \\\\
\\\\
&E & &= %.2e \ N/m^{-2} \\\\
&I_{y} & &= %.2e \ m^{4} \\\\
&f_{e} & &=2/\pi \cdot (3 \cdot E \cdot I_{y}) / \sqrt{0.49 \cdot \mu \cdot l_{ov}^{4}} & &=  %.2f \ Hz \\\\
\\end{align*}$
"""%(g_k, q_k, psi2, L, q, mu, m_mod, E, I_y, f)

md(outp)<jupyter_output><empty_output>
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