F_friction(t) plot for phys.pro/problems/237/

237.py

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import rc, rcParams

from matplotlib.ticker import FuncFormatter
from matplotlib.ticker import MultipleLocator

# Plot setup {{{
lw = 2
k=1.4
rcParams['font.size'] = 23
rcParams['text.usetex'] = True
rcParams['font.sans-serif'] = ['Computer Modern']
rc('text.latex', preamble=r'\usepackage[T2A]{fontenc} \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{bm}')

rc('axes', linewidth=lw)
rc('xtick.major', size=4, width=lw)
rc('ytick.major', size=4, width=lw)
fig, ax = plt.subplots(figsize=(12,7))
fig.subplots_adjust(left=.20, bottom=.13, right=.90, top=.68)

# Set comma as a decimal separator (bad)
import locale
locale.setlocale(locale.LC_NUMERIC, 'ru_RU')
rcParams['axes.formatter.use_locale'] = True
def format_decimal(value, tick_number):
    value = round(value, 2) # Fixes 0,60000000000001 instead of 0,6
    return '$' + str(value).replace('.', '{,}') + '$'
#ax.yaxis.set_major_formatter(FuncFormatter(format_decimal))
#ax.xaxis.set_major_formatter(FuncFormatter(format_decimal))
#}}}

# Set parameters
m = 2  # kg
R = 1  # m
g = 10 # m/s²
a = np.radians(30) # deg

T = 5 # s
w = 2*np.pi / T # rad/s

t = np.linspace(0, 2*T, 1000)
F = m*g* np.sqrt( (w**2*R/g)**2 + 2*w**2*R*np.sin(a)/g * np.cos(w*t) + np.sin(a)**2)

R_values = np.array([0.3*g*np.sin(a)/w**2, g*np.sin(a)/w**2, 2*g*np.sin(a)/w**2, 3*g*np.sin(a)/w**2])
colormap = plt.cm.get_cmap('Blues')
normalize = plt.Normalize(R_values.min()-3.0, R_values.max())


for R in R_values:
    F = m * g * np.sqrt((w**2 * R/g)**2 + 2 * w**2 * R * np.sin(a)/g * np.cos(w*t) + np.sin(a)**2)
    ax.plot(t, F, label=r'$m\omega^2R={}\cdot mg\sin\alpha$'.format(round(w**2*R/(g*np.sin(a)), 1)).replace('.', '{,}'),
            lw=lw, color=colormap(normalize(R)))
    print (R)

## Add colorbar
#sm = plt.cm.ScalarMappable(cmap=colormap, norm=plt.Normalize(R_values.min(), R_values.max()))
#sm.set_array([])
#cbar = plt.colorbar(sm, label=r'$R$')

ax.set_xlabel(r'$t, \textrm{с}$')
ax.set_ylabel(r'$F_\textrm{тр},\;\textrm{Н}$', labelpad=13)

ax.grid()

ax.legend(loc='upper center', bbox_to_anchor=(0.5, 1.6),
          ncol=1, fancybox=False, shadow=False)

#ax.yaxis.set_major_locator(plt.MaxNLocator(5))
#ax.xaxis.set_major_locator(plt.MaxNLocator(6))

ax.set_ylim([0,42])

plt.show()