human
What is a Python program to find the eigenvalues and eigenvectors for three masses given the following:
I am working on the file "P10-CoupledMasses.ipynb".
The first task is:
Project 10 (option A)
Complete the analyss of three masses connected by springs of equal spring constant.
Find the eigenvalues and eigenvectors for three masses.
Use the RK4 approach as shown above to validate that the eigenvalues you compute are correct.
Can you write Python program for it?
assistant
#Here is Python program to find the eigenvalues and eigenvectors for three masses.

from scipy.optimize import curve_fit

def cosFit(t, A, omega, phi):
    """
    Function def for a cosine fit
    """
    return A*np.cos(omega*t+phi)

x1a=np.array(x1list)
ta=np.array(tlist)
popt, pcov = curve_fit(cosFit, ta, x1a, p0=(0.707, np.sqrt(10.0), 0.0))

A=popt[0]
omega=popt[1]
phi=popt[2]

print("A =>", A)
print("omega**2 =>", omega**2)
print("phi =>", phi)

pl.title('Fit to find frequency.')
pl.xlabel('t')
pl.ylabel('x1')
pl.plot(ta, cosFit(ta, A, omega, phi), 'b-', label="fit")
pl.plot(ta, x1a, 'r.', label='data')
pl.legend()