Calculo+de+Datos-Ecuaciones+Empiricas-CEPREU-UPAO (2)
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Mesa Nº01 Ecuaciones Empiricas-Pendulo Simple Nº Oscilaciones 5 Nº Mediciones 10 Tabla Nº01 para el Grafico T vs L Tabla Nº02: Ecuacion Linealizada LnT vs LnL N L(cm) T (s) N L(cm) T(s) X=Ln L Y=Ln T 1 20 0.906 0.880 0.920 0.942 0.932 0.9160 1 20 0.9160 2.9957 -0.0877 Ecuacion d 2 25 1.042 1.054 1.070 1.042 1.034 1.0484 2 25 1.0484 3.2189 0.0473 Ecuacion seg 3 30 1.144 1.106 1.116 1.084 1.122 1.1144 3 30 1.1144 3.4012 0.1083 Linealizamos la ecuación: 4 40 1.278 1.270 1.304 1.304 1.310 1.2932 4 40 1.2932 3.6889 0.2571 9.81 5 50 1.430 1.406 1.428 1.420 1.438 1.4244 5 50 1.4244 3.9120 0.3538 6 60 1.582 1.594 1.594 1.670 1.582 1.6044 6 60 1.6044 4.0943 0.4727 LnT=Lnk+nLnL 7 70 1.702 1.732 1.678 1.716 1.724 1.7104 7 70 1.7104 4.2485 0.5367 8 80 1.846 1.850 1.838 1.812 1.824 1.8340 8 80 1.8340 4.3820 0.6065 Y=A+BX Ec. General de l 9 90 1.916 1.902 1.934 1.880 1.910 1.9084 9 90 1.9084 4.4998 0.6463 10 100 2.028 2.012 2.020 1.990 1.998 2.0096 10 100 2.0096 4.6052 0.6979 Y=lnT ; A=lnk ;B=n, X=LnL Método Estadístico aplicado en la ecuacion linealizada Tabla Nº03: N X=Ln L Y=Ln T XY 1 2.9957 -0.0877 -0.2628 8.9744 0.0077 2.8363 2 3.2189 0.0473 0.1521 10.3612 0.0022 2.1024 3 3.4012 0.1083 0.3684 11.5681 0.0117 1.9149 4 3.6889 0.2571 0.9485 13.6078 0.0661 1.3134 5 3.9120 0.3538 1.3839 15.3039 0.1251 1.0189 6 4.0943 0.4727 1.9356 16.7637 0.2235 0.6336 Calculo del Intercepto(A) y la Pendiente(B) con comandos Excel:interseccion.eje y pendiente 7 4.2485 0.5367 2.2803 18.0497 0.2881 0.5021 8 4.3820 0.6065 2.6577 19.2022 0.3678 0.3558 A= -1.541 s K= 0.214 9 4.4998 0.6463 2.9081 20.2483 0.4177 0.3057 B= 0.4878 s/m n=B n= 0.488 10 4.6052 0.6979 3.2141 21.2076 0.4871 0.2237 39.0466 3.6389 15.5858 155.2869 1.9971 11.2068 1.184 LnT = -1.541 + 0.488 LnL Ec. Linealizada 2.776 Error de A A= -1.541 0.704 Error de B T = 0.214 ( L ) 0.488 Ec. Empirica del Pendulo Simple B= 0.488 T1 (s) T2 (s) T3 (s) T4 (s) T5 (s) Y=kX n T=kL n LnT=Ln(kL n ) Gravedad (g) m/s 2 X 2 Y 2 K=e A δy = ΔA= ΔB= ( Y−BX−AY) 2 10 20 30 40 50 60 70 80 90 100 110 0.0000 0.5000 1.0000 1.5000 2.0000 2.5000 f(x) = 0.2142399976966 x^0.4877632532249 T vs L 2.5000 3.0000 3.5000 4.0000 4.5000 5.0000 -0.2000 0.0000 0.2000 0.4000 0.6000 0.8000 f(x) = 0.4877632532 x − 1.5406584078 LnT vs LnL Usuario: Var. Indep.(X) Usuario: Var. Dep. (Y)
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Transcript of Calculo+de+Datos-Ecuaciones+Empiricas-CEPREU-UPAO (2)
Mesa 01Mesa N01Ecuaciones Empiricas-Pendulo SimpleN Oscilaciones5N Mediciones10Tabla N01 para el Grafico T vs LTabla N02: Ecuacion Linealizada LnT vs LnLNL(cm)T1 (s)T2 (s)T3 (s)T4 (s)T5 (s)T (s)NL(cm)T(s)X=Ln LY=Ln T1200.9060.8800.9200.9420.9320.91601200.91602.9957-0.0877Y=kXnEcuacion de la Curva Tipo Potencial2251.0421.0541.0701.0421.0341.04842251.04843.21890.0473T=kLnEcuacion segn los datos Experimentales3301.1441.1061.1161.0841.1221.11443301.11443.40120.1083Linealizamos la ecuacin:4401.2781.2701.3041.3041.3101.29324401.29323.68890.2571LnT=Ln(kLn)Gravedad (g)9.81m/s25501.4301.4061.4281.4201.4381.42445501.42443.91200.35386601.5821.5941.5941.6701.5821.60446601.60444.09430.4727LnT=Lnk+nLnL7701.7021.7321.6781.7161.7241.71047701.71044.24850.53678801.8461.8501.8381.8121.8241.83408801.83404.38200.6065Y=A+BXEc. General de la recta9901.9161.9021.9341.8801.9101.90849901.90844.49980.6463101002.0282.0122.0201.9901.9982.0096101002.00964.60520.6979Y=lnT ; A=lnk ;B=n, X=LnLMtodo Estadstico aplicado en la ecuacion linealizadaTabla N03:NX=Ln LY=Ln TXYX2Y212.9957-0.0877-0.26288.97440.00772.836323.21890.04730.152110.36120.00222.102433.40120.10830.368411.56810.01171.914943.68890.25710.948513.60780.06611.313453.91200.35381.383915.30390.12511.018964.09430.47271.935616.76370.22350.6336Calculo del Intercepto(A) y la Pendiente(B) con comandos Excel:interseccion.eje y pendiente74.24850.53672.280318.04970.28810.502184.38200.60652.657719.20220.36780.3558A=-1.5406584078sK=eAK=0.21494.49980.64632.908120.24830.41770.3057B=0.4877632532s/mn=Bn=0.488104.60520.69793.214121.20760.48710.223739.04663.638915.5858155.28691.997111.2068y =1.184LnT=-1.541+0.488LnLEc. LinealizadaA=2.776Error de AA=-1.541B=0.704Error de BT=0.214( L )0.488Ec. Empirica del Pendulo SimpleB=0.488
Usuario:Var. Indep.(X)Usuario:Var. Dep. (Y)
Mesa 01
T vs L
Mesa 02
LnT vs LnL
Mesa 03Mesa N02Ecuaciones Empiricas-Pendulo SimpleN Oscilaciones5N Mediciones10Tabla N01 para el Grafico T vs LTabla N02: Ecuacion Linealizada LnT vs LnLNL(cm)T1 (s)T2 (s)T3 (s)T4 (s)T5 (s)T (s)NL(cm)T(s)X=Ln LY=Ln T1200.8400.8080.9220.8580.8700.85961200.85962.9957-0.1513Y=kXnEcuacion de la Curva Tipo Potencial2250.8700.9940.8700.8840.8300.88962250.88963.2189-0.1170T=kLnEcuacion segn los datos Experimentales3300.9020.9220.9160.8840.9320.91123300.91123.4012-0.0930Linealizamos la ecuacin:4401.0401.0201.0541.0701.0341.04364401.04363.68890.0427LnT=Ln(kLn)Gravedad (g)9.81m/s25501.1781.1341.1341.1421.1021.13805501.13803.91200.12936601.2381.2661.2701.2601.2341.25366601.25364.09430.2260LnT=Lnk+nLnL7701.3721.3061.3541.3601.3181.34207701.34204.24850.29428801.4561.4201.4701.4201.4781.44888801.44884.38200.3707Y=A+BXEc. General de la recta9901.5001.5401.5421.5341.5221.52769901.52764.49980.4237101001.6321.5901.5821.6061.6601.6140101001.61404.60520.4787Y=lnT ; A=lnk ;B=n, X=LnLMtodo Estadstico aplicado en la ecuacion linealizadaTabla N03:NX=Ln LY=Ln TXYX2Y212.9957-0.1513-0.45328.97440.02292.581023.2189-0.1170-0.376610.36120.01372.606833.4012-0.0930-0.316311.56810.00862.660143.68890.04270.157413.60780.00182.008553.91200.12930.505715.30390.01671.682464.09430.22600.925416.76370.05111.2887Calculo del Intercepto(A) y la Pendiente(B) con comandos Excel:interseccion.eje y pendiente74.24850.29421.249718.04970.08651.064784.38200.37071.624619.20220.13740.8087A=-1.450400706sK=eAK=0.23494.49980.42371.906620.24830.17950.6693B=0.412533735s/mn=Bn=0.413104.60520.47872.204621.20760.22920.528239.04661.60407.4279155.28690.747515.8983y =1.410LnT=-1.450+0.413LnLEc. LinealizadaA=3.306Error de AA=-1.450B=0.839Error de BT=0.234( L )0.413Ec. Empirica del Pendulo SimpleB=0.413
Usuario:Var. Indep.(X)Usuario:Var. Dep. (Y)
Mesa 03
T vs L
Mesa 04
LnT vs LnL
Mesa 05Mesa N04Ecuaciones Empiricas-Pendulo SimpleN Oscilaciones5N Mediciones10Tabla N01 para el Grafico T vs LTabla N02: Ecuacion Linealizada LnT vs LnLNL(cm)T1 (s)T2 (s)T3 (s)T4 (s)T5 (s)T (s)NL(cm)T(s)X=Ln LY=Ln T1200.9460.8220.8660.8060.7520.83841200.83842.9957-0.1763Y=kXnEcuacion de la Curva Tipo Potencial2250.8440.8600.8780.8080.8060.83922250.83923.2189-0.1753T=kLnEcuacion segn los datos Experimentales3300.9340.9300.9420.9420.9460.93883300.93883.4012-0.0632Linealizamos la ecuacin:4401.0221.0541.0201.0541.0301.03604401.03603.68890.0354LnT=Ln(kLn)Gravedad (g)9.81m/s25501.1441.1921.1721.1681.1461.16445501.16443.91200.15226601.2801.2841.2621.2721.2541.27046601.27044.09430.2393LnT=Lnk+nLnL7701.3941.3481.3481.3681.3661.36487701.36484.24850.31108801.4701.4581.4861.4701.4701.47088801.47084.38200.3858Y=A+BXEc. General de la recta9901.5781.5061.5901.5901.5341.55969901.55964.49980.4444101001.6441.6601.5961.6661.6581.6448101001.64484.60520.4976Y=lnT ; A=lnk ;B=n, X=LnLMtodo Estadstico aplicado en la ecuacion linealizadaTabla N03:NX=Ln LY=Ln TXYX2Y212.9957-0.1763-0.52808.97440.03113.186323.2189-0.1753-0.564310.36120.03073.541033.4012-0.0632-0.214811.56810.00402.803943.68890.03540.130513.60780.00132.399753.91200.15220.595415.30390.02321.816964.09430.23930.979916.76370.05731.4521Calculo del Intercepto(A) y la Pendiente(B) con comandos Excel:interseccion.eje y pendiente74.24850.31101.321318.04970.09671.186584.38200.38581.690619.20220.14880.9146A=-1.5708625241sK=eAK=0.20894.49980.44441.999820.24830.19750.7362B=0.4445891324s/mn=Bn=0.445104.60520.49762.291621.20760.24760.590039.04661.65107.7021155.28690.838218.6272y =1.526LnT=-1.571+0.445LnLEc. LinealizadaA=3.578Error de AA=-1.571B=0.908Error de BT=0.208( L )0.445Ec. Empirica del Pendulo SimpleB=0.445
Usuario:Var. Indep.(X)Usuario:Var. Dep. (Y)
Mesa 05
T vs L
Mesa 06
LnT vs LnL
Mesa N03Ecuaciones Empiricas-Pendulo SimpleN Oscilaciones5N Mediciones10Tabla N01 para el Grafico T vs LTabla N02: Ecuacion Linealizada LnT vs LnLNL(cm)T1 (s)T2 (s)T3 (s)T4 (s)T5 (s)T (s)NL(cm)T(s)X=Ln LY=Ln T1200.8000.9000.8000.9000.9000.86001200.86002.9957-0.1508Y=kXnEcuacion de la Curva Tipo Potencial2251.0001.0001.0001.0001.0001.00002251.00003.21890.0000T=kLnEcuacion segn los datos Experimentales3301.1001.0001.1001.1001.0001.06003301.06003.40120.0583Linealizamos la ecuacin:4401.2001.2001.2001.2001.2001.20004401.20003.68890.1823LnT=Ln(kLn)Gravedad (g)9.81m/s25501.4001.4001.4001.4001.4001.40005501.40003.91200.33656601.6001.6001.6001.6001.6001.60006601.60004.09430.4700LnT=Lnk+nLnL7701.7001.7001.6001.7001.7001.68007701.68004.24850.51888801.8001.8001.8001.7001.8001.78008801.78004.38200.5766Y=A+BXEc. General de la recta9901.9001.9001.8001.9001.8001.86009901.86004.49980.6206101001.9001.8001.9001.9001.9001.8800101001.88004.60520.6313Y=lnT ; A=lnk ;B=n, X=LnLMtodo Estadstico aplicado en la ecuacion linealizadaTabla N03:NX=Ln LY=Ln TXYX2Y212.9957-0.1508-0.45188.97440.02273.653223.21890.00000.000010.36120.00002.639933.40120.05830.198211.56810.00342.441743.68890.18230.672613.60780.03321.903053.91200.33651.316315.30390.11321.175464.09430.47001.924416.76370.22090.6770Calculo del Intercepto(A) y la Pendiente(B) con comandos Excel:interseccion.eje y pendiente74.24850.51882.204118.04970.26910.595284.38200.57662.526719.20220.33250.4704A=-1.6466032004sK=eAK=0.19394.49980.62062.792520.24830.38510.3956B=0.5047700432s/mn=Bn=0.505104.60520.63132.907121.20760.39850.427539.04663.243514.0900155.28691.778814.3789y =1.341LnT=-1.647+0.505LnLEc. LinealizadaA=3.144Error de AA=-1.647B=0.798Error de BT=0.193( L )0.505Ec. Empirica del Pendulo SimpleB=0.505
Usuario:Var. Indep.(X)Usuario:Var. Dep. (Y)
T vs L
LnT vs LnL
Mesa N05Ecuaciones Empiricas-Pendulo SimpleN Oscilaciones5N Mediciones10Tabla N01 para el Grafico T vs LTabla N02: Ecuacion Linealizada LnT vs LnLNL(cm)T1 (s)T2 (s)T3 (s)T4 (s)T5 (s)T (s)NL(cm)T(s)X=Ln LY=Ln T1200.8300.8200.8400.8400.8100.82801200.82802.9957-0.1887Y=kXnEcuacion de la Curva Tipo Potencial2250.9400.8500.9301.0200.8800.92402250.92403.2189-0.0790T=kLnEcuacion segn los datos Experimentales3301.0700.9900.9000.9100.9200.95803300.95803.4012-0.0429Linealizamos la ecuacin:4401.0201.0401.0701.0501.0701.05004401.05003.68890.0488LnT=Ln(kLn)Gravedad (g)9.81m/s25501.1601.1801.1601.1701.1901.17205501.17203.91200.15876601.2901.2701.2801.3401.2501.28606601.28604.09430.2515LnT=Lnk+nLnL7701.3801.3901.4001.3601.3701.38007701.38004.24850.32218801.4701.4401.4601.4401.4701.45608801.45604.38200.3757Y=A+BXEc. General de la recta9901.5501.5701.5501.5201.5601.55009901.55004.49980.4383101001.6501.6701.6101.6801.6301.6480101001.64804.60520.4996Y=lnT ; A=lnk ;B=n, X=LnLMtodo Estadstico aplicado en la ecuacion linealizadaTabla N03:NX=Ln LY=Ln TXYX2Y212.9957-0.1887-0.56548.97440.03562.971323.2189-0.0790-0.254410.36120.00622.394433.4012-0.0429-0.145911.56810.00182.356243.68890.04880.180013.60780.00242.045253.91200.15870.620915.30390.02521.570564.09430.25151.029916.76370.06331.2127Calculo del Intercepto(A) y la Pendiente(B) con comandos Excel:interseccion.eje y pendiente74.24850.32211.368418.04970.10370.984684.38200.37571.646319.20220.14110.8398A=-1.4625288529sK=eAK=0.23294.49980.43831.972120.24830.19210.6591B=0.4202477865s/mn=Bn=0.420104.60520.49962.300621.20760.24960.497239.04661.78398.1523155.28690.821115.5308y =1.393LnT=-1.463+0.420LnLEc. LinealizadaA=3.268Error de AA=-1.463B=0.829Error de BT=0.232( L )0.420Ec. Empirica del Pendulo SimpleB=0.420
Usuario:Var. Indep.(X)Usuario:Var. Dep. (Y)
T vs L
LnT vs LnL
Mesa N06Ecuaciones Empiricas-Pendulo SimpleN Oscilaciones5N Mediciones10Tabla N01 para el Grafico T vs LTabla N02: Ecuacion Linealizada LnT vs LnLNL(cm)T1 (s)T2 (s)T3 (s)T4 (s)T5 (s)T (s)NL(cm)T(s)X=Ln LY=Ln T1200.7940.9500.8640.8520.8460.86121200.86122.9957-0.1494Y=kXnEcuacion de la Curva Tipo Potencial2250.9101.0400.9820.9941.0540.99602250.99603.2189-0.0040T=kLnEcuacion segn los datos Experimentales3301.0721.0901.0681.0881.0901.08163301.08163.40120.0784Linealizamos la ecuacin:4401.2621.2261.2521.2841.1841.24164401.24163.68890.2164LnT=Ln(kLn)Gravedad (g)9.81m/s25501.4261.4121.3961.5001.3761.42205501.42203.91200.35216601.4941.5061.5401.4601.5161.50326601.50324.09430.4076LnT=Lnk+nLnL7701.6881.7101.6201.6941.6661.67567701.67564.24850.51628801.7801.8201.7601.7581.7281.76928801.76924.38200.5705Y=A+BXEc. General de la recta9901.9401.8881.8621.8502.0261.91329901.91324.49980.6488101002.0941.9722.0922.0402.1002.0596101002.05964.60520.7225Y=lnT ; A=lnk ;B=n, X=LnLMtodo Estadstico aplicado en la ecuacion linealizadaTabla N03:NX=Ln LY=Ln TXYX2Y212.9957-0.1494-0.44768.97440.02233.873823.2189-0.0040-0.012910.36120.00002.861733.40120.07840.266811.56810.00622.446143.68890.21640.798313.60780.04681.799153.91200.35211.377315.30390.12391.190664.09430.40761.668816.76370.16611.0738Calculo del Intercepto(A) y la Pendiente(B) con comandos Excel:interseccion.eje y pendiente74.24850.51622.193018.04970.26640.677784.38200.57052.500119.20220.32550.5566A=-1.7030036565sK=eAK=0.18294.49980.64882.919420.24830.42090.3553B=0.5221738775s/mn=Bn=0.522104.60520.72253.327321.20760.52200.204139.04663.359114.5903155.28691.900315.0386y =1.371LnT=-1.703+0.522LnLEc. LinealizadaA=3.215Error de AA=-1.703B=0.816Error de BT=0.182( L )0.522Ec. Empirica del Pendulo SimpleB=0.522
Usuario:Var. Indep.(X)Usuario:Var. Dep. (Y)
T vs L
LnT vs LnL
MBD00175159.unknown
MBD001753C8.unknown
MBD00175581.unknown
MBD001752BA.unknown
MBD00031CB6.unknown
MBD00174FA7.unknown
