Radians Appendix

Question: Describe about the Radians Appendix? Answer: We have taken around 640 points for calculating the ordinates separated by 0.01 radians. Some of the points are shown in the following table, while rest can be found in the appendix. V1 V2 R 0 121.2436 -100 21.24356 0.01 121.9375 -99.995 21.94248 0.02 122.6192 -99.98 22.63921 0.03 123.2887 -99.955 23.33368 0.04 123.9458 -99.92 24.02582 0.05 124.5906 -99.875 24.71555 0.06 125.2229 -99.8201 25.40281 0.07 125.8426 -99.7551 26.08753 0.08 126.4498 -99.6802 26.76964 0.09 127.0443 -99.5953 27.44908 0.1 127.6262 -99.5004 28.12577 0.11 128.1953 -99.3956 28.79964 0.12 128.7515 -99.2809 29.47064 The graph obtained for the signals and their resultant are shown in the following figure: The magnitude of the resultant can be calculated as : The magnitude of the phase is given as: Using the trapezoidal rule and taking 10 point intervals we have the following values: Interval length(h=0.3) Velocity 1 0.3 17.11 8.555 2 0.6 15.04 15.04 3 0.9 12.79 12.79 4 1.2 10.36 10.36 5 1.5 7.75 7.75 6 1.8 4.96 4.96 7 2.1 1.99 1.99 8 2.4 -1.16 -1.16 9 2.7 -4.49 -4.49 10 3 -8 -4 Sum 51.795 Total distance(sum*h) 15.5385 Average Acceleration: Using the midpoint ordinate rule and taking 10 point intervals we have the following values: Interval length(h=0.3) Mid points 1 0.3 0.45 16.0975 2 0.6 0.75 13.9375 3 0.9 1.05 11.5975 4 1.2 1.35 9.0775 5 1.5 1.65 6.3775 6 1.8 1.95 3.4975 7 2.1 2.25 0.4375 8 2.4 2.55 -2.8025 9 2.7 2.85 -6.2225 10 3 Sum 51.9975 Total Distance(sum*h) 15.59925 Average Acceleration: Using the Simpson rule and taking 10 point intervals we have the following values: Interval length(0.3) Velocity Ordinate points 1 0.3 17.11 8.555 8.555 2 0.6 15.04 15.04 60.16 3 0.9 12.79 12.79 25.58 4 1.2 10.36 10.36 41.44 5 1.5 7.75 7.75 15.5 6 1.8 4.96 4.96 19.84 7 2.1 1.99 1.99 3.98 8 2.4 -1.16 -1.16 -4.64 9 2.7 -4.49 -4.49 -8.98 10 3 -8 -4 -4 Sum 157.435 Distance(sum*h/3) 15.7435 Average Acceleration: The calculus method: Average Acceleration: For the calculus method gives the correct result the number of points taken should be more to achieve the result closer to calculus values. The Simpsons value is the most closer. The technologies like spreadsheet hep in calculating more points and hence help in achieving the values closer to the actual. Appendix V1 V2 R 0 121.2436 -100 21.24356 0.01 121.9375 -99.995 21.94248 0.02 122.6192 -99.98 22.63921 0.03 123.2887 -99.955 23.33368 0.04 123.9458 -99.92 24.02582 0.05 124.5906 -99.875 24.71555 0.06 125.2229 -99.8201 25.40281 0.07 125.8426 -99.7551 26.08753 0.08 126.4498 -99.6802 26.76964 0.09 127.0443 -99.5953 27.44908 0.1 127.6262 -99.5004 28.12577 0.11 128.1953 -99.3956 28.79964 0.12 128.7515 -99.2809 29.47064 0.13 129.2949 -99.1562 30.13869 0.14 129.8253 -99.0216 30.80373 0.15 130.3428 -98.8771 31.46568 0.16 130.8472 -98.7227 32.12449 0.17 131.3386 -98.5585 32.78009 0.18 131.8168 -98.3844 33.43241 0.19 132.2818 -98.2004 34.08139 0.2 132.7336 -98.0067 34.72695 0.21 133.1721 -97.8031 35.36905 0.22 133.5974 -97.5897 36.00761 0.23 134.0092 -97.3666 36.64256 0.24 134.4077 -97.1338 37.27386 0.25 134.7927 -96.8912 37.90142 0.26 135.1642 -96.639 38.5252 0.27 135.5222 -96.3771 39.14512 0.28 135.8667 -96.1055 39.76113 0.29 136.1976 -95.8244 40.37316 0.3 136.5148 -95.5336 40.98116 0.31 136.8184 -95.2334 41.58506 0.32 137.1083 -94.9235 42.1848 0.33 137.3846 -94.6042 42.78032 0.34 137.647 -94.2755 43.37156 0.35 137.8957 -93.9373 43.95846 0.36 138.1307 -93.5897 44.54097 0.37 138.3518 -93.2327 45.11903 0.38 138.559 -92.8665 45.69257 0.39 138.7525 -92.4909 46.26155 0.4 138.932 -92.1061 46.8259 0.41 139.0976 -91.7121 47.38556 0.42 139.2494 -91.3089 47.94049 0.43 139.3872 -90.8966 48.49062 0.44 139.5111 -90.4752 49.03591 0.45 139.621 -90.0447 49.57629 0.46 139.717 -89.6052 50.11171 0.47 139.799 -89.1568 50.64212 0.48 139.867 -88.6995 51.16747 0.49 139.921 -88.2333 51.6877 0.5 139.961 -87.7583 52.20276 0.51 139.9871 -87.2745 52.7126 0.52 139.9991 -86.7819 53.21718 0.53 139.9971 -86.2807 53.71642 0.54 139.9812 -85.7709 54.2103 0.55 139.9512 -85.2525 54.69876 0.56 139.9073 -84.7255 55.18175 0.57 139.8493 -84.1901 55.65921 0.58 139.7774 -83.6463 56.13112 0.59 139.6915 -83.0941 56.59741 0.6 139.5916 -82.5336 57.05804 0.61 139.4778 -81.9648 57.51296 0.62 139.35 -81.3878 57.96213 0.63 139.2083 -80.8028 58.40551 0.64 139.0526 -80.2096 58.84305 0.65 138.8831 -79.6084 59.2747 0.66 138.6996 -78.9992 59.70042 0.67 138.5023 -78.3822 60.12018 0.68 138.2912 -77.7573 60.53392 0.69 138.0662 -77.1246 60.94161 0.7 137.8274 -76.4842 61.34321 0.71 137.5749 -75.8362 61.73867 0.72 137.3085 -75.1806 62.12795 0.73 137.0285 -74.5174 62.51103 0.74 136.7347 -73.8469 62.88785 0.75 136.4273 -73.1689 63.25839 0.76 136.1062 -72.4836 63.6226 0.77 135.7715 -71.7911 63.98044 0.78 135.4232 -71.0914 64.33189 0.79 135.0614 -70.3845 64.67691 0.8 134.6861 -69.6707 65.01545 0.81 134.2973 -68.9498 65.3475 0.82 133.8951 -68.2221 65.67301 0.83 133.4795 -67.4876 65.99196 0.84 133.0506 -66.7463 66.3043 0.85 132.6083 -65.9983 66.61002 0.86 132.1528 -65.2437 66.90907 0.87 131.6841 -64.4827 67.20143 0.88 131.2022 -63.7151 67.48708 0.89 130.7072 -62.9412 67.76597 0.9 130.1991 -62.161 68.03809 0.91 129.678 -61.3746 68.3034 0.92 129.1439 -60.582 68.56189 0.93 128.5969 -59.7834 68.81352 0.94 128.0371 -58.9788 69.05826 0.95 127.4644 -58.1683 69.2961 0.96 126.879 -57.352 69.52701 0.97 126.2809 -56.53 69.75097 0.98 125.6702 -55.7023 69.96796 0.99 125.0469 -54.869 70.17794 1 124.4111 -54.0302 70.38091 1.01 123.7629 -53.1861 70.57684 1.02 123.1023 -52.3366 70.76572 1.03 122.4294 -51.4819 70.94751 1.04 121.7442 -50.622 71.12221 1.05 121.0469 -49.7571 71.2898 1.06 120.3375 -48.8872 71.45027 1.07 119.616 -48.0124 71.60358 1.08 118.8826 -47.1328 71.74974 1.09 118.1373 -46.2485 71.88872 1.1 117.3801 -45.3596 72.02051 1.11 116.6113 -44.4662 72.1451 1.12 115.8307 -43.5682 72.26248 1.13 115.0386 -42.666 72.37263 1.14 114.235 -41.7595 72.47554 1.15 113.4199 -40.8487 72.5712 1.16 112.5936 -39.934 72.65961 1.17 111.7559 -39.0152 72.74075 1.18 110.9071 -38.0925 72.81462 1.19 110.0472 -37.166 72.88121 1.2 109.1763 -36.2358 72.9405 1.21 108.2944 -35.3019 72.99251 1.22 107.4018 -34.3646 73.03721 1.23 106.4984 -33.4238 73.07461 1.24 105.5843 -32.4796 73.10471 1.25 104.6597 -31.5322 73.12749 1.26 103.7247 -30.5817 73.14296 1.27 102.7792 -29.6281 73.15112 1.28 101.8235 -28.6715 73.15196 1.29 100.8576 -27.7121 73.14549 1.3 99.88158 -26.7499 73.1317 1.31 98.8956 -25.785 73.1106 1.32 97.89973 -24.8175 73.08219 1.33 96.89407 -23.8476 73.04647 1.34 95.87872 -22.8753 73.00344 1.35 94.85378 -21.9007 72.95312 1.36 93.81936 -20.9239 72.8955 1.37 92.77556 -19.945 72.83059 1.38 91.72248 -18.9641 72.75839 1.39 90.66022 -17.9813 72.67892 1.4 89.5889 -16.9967 72.59219 1.41 88.50862 -16.0104 72.49819 1.42 87.41949 -15.0225 72.39695 1.43 86.32162 -14.0332 72.28846 1.44 85.21512 -13.0424 72.17275 1.45 84.10009 -12.0503 72.04982 1.46 82.97666 -11.057 71.91968 1.47 81.84493 -10.0626 71.78235 1.48 80.70501 -9.06716 71.63785 1.49 79.55702 -8.07084 71.48618 1.5 78.40108 -7.07372 71.32736 1.51 77.2373 -6.07589 71.16141 1.52 76.06579 -5.07745 70.98834 1.53 74.88668 -4.0785 70.80817 1.54 73.70007 -3.07915 70.62093 1.55 72.5061 -2.07948 70.42662 1.56 71.30488 -1.07961 70.22527 1.57 70.09653 -0.07963 70.01689 1.58 68.88116 0.920354 69.80152 1.59 67.65891 1.920249 69.57916 1.6 66.4299 2.919952 69.34985 1.61 65.19424 3.919363 69.1136 1.62 63.95206 4.918382 68.87044 1.63 62.70349 5.916909 68.6204 1.64 61.44864 6.914845 68.36349 1.65 60.18765 7.912089 68.09974 1.66 58.92065 8.908542 67.82919 1.67 57.64775 9.904104 67.55185 1.68 56.36908 10.89868 67.26776 1.69 55.08478 11.89216 66.97694 1.7 53.79497 12.88445 66.67942 1.71 52.49978 13.87545 66.37524 1.72 51.19934 14.86507 66.06441 1.73 49.89379 15.8532 65.74699 1.74 48.58324 16.83974 65.42298 1.75 47.26783 17.82461 65.09244 1.76 45.9477 18.80768 64.75538 1.77 44.62297 19.78888 64.41185 1.78 43.29378 20.7681 64.06188 1.79 41.96026 21.74524 63.7055 1.8 40.62254 22.72021 63.34275 1.81 39.28077 23.6929 62.97367 1.82 37.93506 24.66323 62.59829 1.83 36.58556 25.63109 62.21665 1.84 35.2324 26.59639 61.82879 1.85 33.87572 27.55902 61.43475 1.86 32.51565 28.51891 61.03456 1.87 31.15233 29.47594 60.62827 1.88 29.7859 30.43002 60.21592 1.89 28.41648 31.38106 59.79754 1.9 27.04423 32.32896 59.37319 1.91 25.66927 33.27362 58.94289 1.92 24.29174 34.21497 58.50671 1.93 22.91179 35.15288 58.06467 1.94 21.52954 36.08729 57.61683 1.95 20.14514 37.01808 57.16322 1.96 18.75872 37.94518 56.7039 1.97 17.37043 38.86848 56.23891 1.98 15.98041 39.78789 55.76829 1.99 14.58878 40.70332 55.2921 2 13.1957 41.61468 54.81038 2.01 11.80129 42.52189 54.32318 2.02 10.40571 43.42483 53.83054 2.03 9.009085 44.32344 53.33253 2.04 7.611559 45.21762 52.82918 2.05 6.213273 46.10727 52.32054 2.06 4.814365 46.99231 51.80668 2.07 3.414976 47.87265 51.28763 2.08 2.015245 48.74821 50.76345 2.09 0.615312 49.61889 50.2342 2.1 -0.78468 50.48461 49.69993 2.11 -2.1846 51.34528 49.16068 2.12 -3.58429 52.20082 48.61652 2.13 -4.98363 53.05113 48.0675 2.14 -6.38247 53.89614 47.51367 2.15 -7.78067 54.73577 46.95509 2.16 -9.1781 55.56991 46.39182 2.17 -10.5746 56.39851 45.8239 2.18 -11.9701 57.22146 45.2514 2.19 -13.3643 58.03869 44.67438 2.2 -14.7572 58.85011 44.09289 2.21 -16.1487 59.65565 43.50699 2.22 -17.5385 60.45523 42.91674 2.23 -18.9266 61.24876 42.3222 2.24 -20.3127 62.03616 41.72343 2.25 -21.6969 62.81736 41.12048 2.26 -23.0789 63.59228 40.51342 2.27 -24.4585 64.36084 39.90231 2.28 -25.8358 65.12297 39.28722 2.29 -27.2104 65.87858 38.66819 2.3 -28.5823 66.6276 38.04529 2.31 -29.9514 67.36996 37.41859 2.32 -31.3174 68.10559 36.78815 2.33 -32.6804 68.8344 36.15403 2.34 -34.04 69.55633 35.5163 2.35 -35.3963 70.27131 34.87501 2.36 -36.749 70.97926 34.23024 2.37 -38.0981 71.68011 33.58204 2.38 -39.4433 72.37379 32.93048 2.39 -40.7846 73.06023 32.27563 2.4 -42.1218 73.73937 31.61756 2.41 -43.4548 74.41114 30.95632 2.42 -44.7835 75.07546 30.29199 2.43 -46.1077 75.73228 29.62462 2.44 -47.4272 76.38152 28.9543 2.45 -48.742 77.02313 28.28108 2.46 -50.052 77.65703 27.60503 2.47 -51.3569 78.28317 26.92622 2.48 -52.6568 78.90147 26.24472 2.49 -53.9513 79.51189 25.56059 2.5 -55.2405 80.11436 24.87391 2.51 -56.5241 80.70882 24.18474 2.52 -57.8021 81.2952 23.49315 2.53 -59.0742 81.87346 22.79922 2.54 -60.3405 82.44353 22.103 2.55 -61.6008 83.00535 21.40457 2.56 -62.8549 83.55888 20.704 2.57 -64.1027 84.10405 20.00136 2.58 -65.3441 84.6408 19.29673 2.59 -66.5789 85.1691 18.59016 2.6 -67.8071 85.68888 17.88173 2.61 -69.0286 86.20008 17.17152 2.62 -70.2431 86.70267 16.45958 2.63 -71.4506 87.19659 15.74601 2.64 -72.6509 87.68179 15.03085 2.65 -73.844 88.15822 14.3142 2.66 -75.0297 88.62583 13.59611 2.67 -76.2079 89.08459 12.87666 2.68 -77.3785 89.53443 12.15593 2.69 -78.5413 89.97532 11.43398 2.7 -79.6963 90.40721 10.71088 2.71 -80.8433 90.83007 9.986719 2.72 -81.9823 91.24384 9.261556 2.73 -83.113 91.64848 8.535466 2.74 -84.2354 92.04396 7.808523 2.75 -85.3494 92.43024 7.0808 2.76 -86.4549 92.80727 6.352368 2.77 -87.5517 93.17502 5.623301 2.78 -88.6398 93.53346 4.893671 2.79 -89.719 93.88254 4.163552 2.8 -90.7892 94.22223 3.433017 2.81 -91.8504 94.55251 2.702138 2.82 -92.9023 94.87332 1.97099 2.83 -93.945 95.18465 1.239644 2.84 -94.9783 95.48646 0.508174 2.85 -96.0021 95.77872 -0.22335 2.86 -97.0163 96.06141 -0.95484 2.87 -98.0207 96.33449 -1.68625 2.88 -99.0154 96.59793 -2.41748 2.89 -100 96.85172 -3.14847 2.9 -100.975 97.09582 -3.87915 2.91 -101.94 97.33021 -4.60944 2.92 -102.894 97.55486 -5.33927 2.93 -103.838 97.76977 -6.06856 2.94 -104.772 97.97489 -6.79725 2.95 -105.695 98.17022 -7.52526 2.96 -106.608 98.35573 -8.25252 2.97 -107.51 98.53141 -8.97895 2.98 -108.402 98.69723 -9.70448 2.99 -109.282 98.85318 -10.429 3 -110.152 98.99925 -11.1526 3.01 -111.01 99.13542 -11.875 3.02 -111.858 99.26167 -12.5962 3.03 -112.694 99.378 -13.3161 3.04 -113.519 99.48439 -14.0348 3.05 -114.333 99.58083 -14.752 3.06 -115.135 99.66732 -15.4677 3.07 -115.926 99.74383 -16.1819 3.08 -116.705 99.81038 -16.8945 3.09 -117.472 99.86694 -17.6054 3.1 -118.228 99.91352 -18.3145 3.11 -118.972 99.9501 -19.0218 3.12 -119.704 99.97669 -19.7272 3.13 -120.424 99.99328 -20.4307 3.14 -121.132 99.99987 -21.132 3.15 -121.828 99.99647 -21.8313 3.16 -122.511 99.98306 -22.5284 3.17 -123.183 99.95965 -23.2232 3.18 -123.842 99.92625 -23.9157 3.19 -124.489 99.88286 -24.6059 3.2 -125.123 99.82948 -25.2935 3.21 -125.745 99.76611 -25.9787 3.22 -126.354 99.69277 -26.6612 3.23 -126.951 99.60946 -27.341 3.24 -127.534 99.51619 -28.0182 3.25 -128.105 99.41297 -28.6925 3.26 -128.664 99.2998 -29.364 3.27 -129.209 99.17671 -30.0325 3.28 -129.742 99.0437 -30.698 3.29 -130.261 98.90078 -31.3605 3.3 -130.768 98.74798 -32.0198 3.31 -131.261 98.5853 -32.6759 3.32 -131.741 98.41276 -33.3287 3.33 -132.209 98.23038 -33.9783 3.34 -132.663 98.03817 -34.6244 3.35 -133.103 97.83617 -35.267 3.36 -133.531 97.62438 -35.9061 3.37 -133.945 97.40282 -36.5417 3.38 -134.345 97.17153 -37.1736 3.39 -134.732 96.93052 -37.8017 3.4 -135.106 96.67982 -38.4261 3.41 -135.466 96.41945 -39.0467 3.42 -135.813 96.14944 -39.6633 3.43 -136.146 95.86981 -40.276 3.44 -136.465 95.58059 -40.8846 3.45 -136.771 95.28182 -41.4892 3.46 -137.063 94.97352 -42.0896 3.47 -137.341 94.65572 -42.6858 3.48 -137.606 94.32846 -43.2777 3.49 -137.857 93.99176 -43.8653 3.5 -138.094 93.64567 -44.4485 3.51 -138.317 93.29021 -45.0273 3.52 -138.527 92.92542 -45.6015 3.53 -138.723 92.55134 -46.1712 3.54 -138.904 92.168 -46.7363 3.55 -139.072 91.77545 -47.2967 3.56 -139.226 91.37372 -47.8524 3.57 -139.366 90.96285 -48.4033 3.58 -139.492 90.54289 -48.9494 3.59 -139.604 90.11387 -49.4906 3.6 -139.703 89.67584 -50.0268 3.61 -139.787 89.22884 -50.558 3.62 -139.857 88.77293 -51.0841 3.63 -139.913 88.30813 -51.6052 3.64 -139.956 87.8345 -52.1211 3.65 -139.984 87.35209 -52.6318 3.66 -139.998 86.86094 -53.1372 3.67 -139.998 86.36111 -53.6373 3.68 -139.985 85.85264 -54.132 3.69 -139.957 85.33559 -54.6213 3.7 -139.915 84.81 -55.1052 3.71 -139.859 84.27594 -55.5835 3.72 -139.79 83.73344 -56.0563 3.73 -139.706 83.18257 -56.5235 3.74 -139.608 82.62338 -56.9851 3.75 -139.497 82.05594 -57.4409 3.76 -139.371 81.48028 -57.891 3.77 -139.232 80.89648 -58.3353 3.78 -139.078 80.30459 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