md = 552.3e-3 dmd = 0.1e-3 rd = 104.9e-3 / 2.0 drd = 0.5e-3 / 2.0 T1 = [24.10, 23.98, 24.18, 24.02, 24.07] T2 = [33.15, 33.50, 33.23, 33.38, 33.09] mbp = 679.00e-3 dmbp = 0.20e-3 T = [[46.56, 46.64, 46.62], [46.75, 46.73, 46.64], [47.54, 47.39, 47.39], [48.39, 48.20, 48.32], [49.96, 50.17, 50.09], [52.50, 52.48, 52.46]] a = [0.0e-3, 5.7e-3, 11.8e-3, 18.6e-3, 29.9e-3, 36.8e-3] da = [0.6e-3, 0.6e-3, 0.6e-3, 0.6e-3, 0.6e-3, 0.6e-3] # Measurement series reduction dT1 = ms.std_dev_m(T1) / 20 T1 = ms.mean_value(T1) / 20 dT2 = ms.std_dev_m(T2) / 20 T2 = ms.mean_value(T2) / 20 dT = [ms.std_dev_m(T[i]) / 20 for i in range(len(T))] T = [ms.mean_value(T[i]) / 20 for i in range(len(T))] # 1.1 Determination of the deflecting force by torque-deflection angle-dependency measurement M = [] dM = [] for i in range(len(m)): M.append(m[i] * g * r) dM.append( ms.sqrt((m[i] * g * dr)**2 + (m[i] * r * dg)**2 + (g * r * dm[i])**2)) Dt = ms.reg_grad(phi, M, dPhi, dM) * 180.0 / ms.pi
pl = 100980.0 dpl = 60.0 t = 982.89 n = 500 s = [8e-3, 16e-3, 21e-3, 26e-3, 34e-3, 38e-3, 42e-3, 48e-3, 50e-3, 54e-3, 58e-3, 60e-3, 64e-3, 67e-3, 70e-3, 73e-3, 76e-3, 78e-3, 81e-3, 84e-3, 85e-3] ds = [3e-3 for i in range(len(s))] sn = 119e-3 dsn = 1e-3 sa = 852e-3 dsa = 3e-3 # Preparation lp = [lpo[i] - lpu[i] for i in range(len(lpo))] dlp = ms.std_dev_m(lp) # "+" ms.sqrt(2) * dlp # If one uses the addition of the systematic and statistic uncertainty, it must be quadratic lp = ms.mean_value(lp) l = lp - rk dl = ms.sqrt(dlp**2 + drk**2) dt = ms.std_dev_e(t0) T0 = ms.mean_value(t0) / n0 n1 = 2 * l * dt / (0.3 * T0 * dl) print() print(ms.val("n1", int(n1 + 0.5))) print() print(ms.val("gl", gl, dgl)) # Simple calculation T = t / n dT = dt / n gs = 4 * ms.pi**2 * l / T**2
fl1 = 1213 dfl1 = 13 fr1 = 1293 dfr1 = 13 fl2 = 1187 dfl2 = 13 fr2 = 1307 dfr2 = 13 bmax1 = 8.3 dbmax1 = 0.3 bmax2 = 4.9 dbmax2 = 0.1 # Measure series reduction dT = ms.std_dev_m(T) / 20 T = ms.mean_value(T) / 20 dT1 = ms.std_dev_m(T1) / 15 T1 = ms.mean_value(T1) / 15 dT2 = ms.std_dev_m(T2) / 10 T2 = ms.mean_value(T2) / 10 print() print(ms.val("T0", T, dT)) print(ms.val("T1", T1, dT1)) print(ms.val("T2", T2, dT2)) # Damping constant calculated with time of half amplitude t1 = n1 * T1 dt1 = ms.sqrt((n1 * dT1)**2 + (T1 * dn1)**2) t2 = n2 * T2
s2 = 160.0e-3 d_s2 = 3.0e-3 s3 = 360.0e-3 d_s3 = 3.0e-3 s4 = 640.0e-3 d_s4 = 3.0e-3 s5 = 60.0e-3 d_s5 = 1.0e-3 s6 = 101e-3 d_s6 = 1.0e-3 s56 = s6 - s5 d_s56 = m.sqrt(d_s6**2 + d_s5**2) # Zeiten tmp = [0.360, 0.365, 0.369, 0.357, 0.361] t1_vz = ms.mean_value(tmp) d_t1_vz = ms.std_dev_m(tmp) tmp = [0.725, 0.730, 0.734, 0.722, 0.725] t2_vz = ms.mean_value(tmp) d_t2_vz = ms.std_dev_m(tmp) tmp = [1.085, 1.091, 1.093, 1.081, 1.085] t3_vz = ms.mean_value(tmp) d_t3_vz = ms.std_dev_m(tmp) tmp = [1.440, 1.445, 1.447, 1.435, 1.438] t4_vz = ms.mean_value(tmp) d_t4_vz = ms.std_dev_m(tmp) tmp = [1.744, 1.746, 1.741, 1.744, 1.740] t5_vz = ms.mean_value(tmp) d_t5_vz = ms.std_dev_m(tmp) tmp = [1.780, 1.782, 1.777, 1.781, 1.777] t6_vz = ms.mean_value(tmp) d_t6_vz = ms.std_dev_m(tmp)
g = 9.81 d = 6.00e-3 U = 501 b = 7.78e-3 p = 9.98e4 sf = [10, 10, 10, 10, 10] tf = [11.64, 13.26, 12.90, 12.33, 12.19] ss = [10, 10, 10, 10, 10] ts = [13.92, 16.16, 15.58, 16.59, 15.88] r = [0.0, 0.0, 0.0, 0.0, 0.0] q = [0.0, 0.0, 0.0, 0.0, 0.0] eta = [0.0, 0.0, 0.0, 0.0, 0.0] for i in range(5): sf[i] *= 5e-5 ss[i] *= 5e-5 r[i] = 3 * m.sqrt((eta0 * sf[i]) / (2 * rho * g * tf[i])) eta[i] = eta0 / (1.0 + b / (r[i] * p)) q[i] = (sf[i] / tf[i] + ss[i] / ts[i]) * 18 * m.pi * d / U * m.sqrt( sf[i] * eta[i]**3 / (2 * tf[i] * rho * g)) print() print(r) print(eta) print(q) print(ms.mean_value(q)) print(ms.std_dev_m(q)) print(ms.std_dev_e(q))
#print(f_mv) #print(d_f_mv) # chromatische Aberration L = 0.65 d_L = 1.0e-3 s1 = [[0.360, 0.363, 0.358], [0.353, 0.359, 0.35]] d_s1 = [0.0, 0.0] s2 = [[0.691, 0.69, 0.69], [0.693, 0.688, 0.693]] d_s2 = [0.0, 0.0] d = [0.0, 0.0] d_d = [0.0, 0.0] f = [0.0, 0.0] d_f = [0.0, 0.0] for i in range(2): d_s1[i] = ms.std_dev_m(s1[i]) s1[i] = ms.mean_value(s1[i]) d_s2[i] = ms.std_dev_m(s2[i]) s2[i] = ms.mean_value(s2[i]) d[i] = s2[i] - s1[i] d_d[i] = m.sqrt(d_s2[i]**2 + d_s1[i]**2) f[i] = (L**2 - d[i]**2) / (4 * L) d_f[i] = m.sqrt(((L**2 + d[i]**2) * d_L / (2 * L))**2 + (d[i] * d_d[i])**2) / (2 * L) sigma = [abs(f[0] - f[1]) / d_f[0], abs(f[0] - f[1]) / d_f[1]] #print() #print(d) #print(d_d) #print() #print(f)