I have an array of displacement values:
A = 6.15980273514821 6.14448346902259 6.08845116089753 6.10237740189123 6.11608152736223 6.09595708310386 6.08721312535112 6.08234899002155 6.06714986110611 6.07783516323856 6.07792347114879 6.06942843038110 6.06019133043305 6.06261550608395 6.06392554207175 6.07403400879634 6.07480165775461 6.06023816732260 6.06413215823230 6.05980866775166 6.06188423198093 6.04539247866406 5.68706601480939 4.73891273276360 3.33633000147301 1.53377736474907 -0.520209410928023 -2.51119577960674 -4.41312227437336 -6.03989364014165 -7.19838227617766 -7.84654759197349 -7.92368071295474 -7.47392854770517 -6.51019780560905 -5.07107069256220 -3.36973422578889 -1.50050787991370 0.434155257792691 2.12215009949313 3.53006148407630 4.49610896364585 4.92744726480430 4.84056078059572 4.19929415413135 3.15383591162506 1.71286595583864 0.0390502408958251 -1.66192845643858 -3.33294692803218 -4.80249308136781 -5.90361702482525 -6.60666839598799 -6.83843319677040 -6.59833738833612 -5.93158620238645 -4.88505199941910 -3.58238928898158 -2.06162498335311 -0.427978306324553 0.962092147565693 2.21079406034967 3.14407320606021 3.65032027290402 3.71648804678824 3.36000706616073 2.65928916279476 1.60114590344026 0.338579806471336 -1.05833481215168 -2.38367221913169 -3.62501491627475 -4.59871735106957 -5.27463472098307 -5.58863040574497 -5.53036784838860 -5.12001863794680 -4.40681325596626 -3.46518774940656 -2.33147881794239 -1.14253025773902 -0.00120193018594039 1.05416533403683 1.83655243804809 2.34317552443391 2.51855601770804 2.35120342999738 1.90235109235008 1.20233485658391 0.313322912257294 -0.653990145486640 -1.69393994166169 -2.63711164436859 -3.42076266517382 -4.02060849879423 -4.33535045567851 -4.36763583177268 -4.13384363802889 -3.71579617090779 -3.09613185931849 -2.32897335309416 -1.52312351601432 -0.701703723373771 0.0711680436921752 0.672844202931666 1.10019974546121 1.29362318476486 1.24624021443152 1.00403874870039 0.578535494879244 0.0570974441039399 -0.533999805458487 -1.25937401298772 -1.89751921254205 -2.43726901746249 -2.86612610147998 -3.10413193915387 -3.17648524812527 -3.09292469052149 -2.86041286479119 -2.51737566053157 -2.07827258343221 -1.59714345763504 -1.12131785748468 -0.684853319666407 -0.311635411569174 -0.0471022387485308 0.124943852858797 0.127457738929030 0.0209992133123575 -0.216932487595427 -0.456658041475563 -0.764024038661157 -1.10649998879281 -1.39863622698775 -1.67789062705118 -1.88198237554644 -2.01286200701089 -2.05199182485704 -2.00598298730182 -1.92968767887397 -1.78696046276908 -1.64438292043114 -1.48021633242652 -1.31952886260734 -1.18885615969264 -1.07703421305764 -1.01084132179629 -0.971420999249929 -0.978062595741639 -1.01633916058985 -1.05795798469255 -1.09667325981377 -1.11085346887283 -1.12409055761398 -1.12016261878873 -1.10103924041538 -1.11490152792194 -1.11030180564636 -1.10262398739387 -1.11600110094369 -1.10915545278102 -1.12224635477858 -1.10928290200281 -1.11456953961204 -1.11506577559769 -1.10755461106175 -1.10241423280547 -1.11201076964811 -1.10010826509149 -1.11036709193206 -1.11166169215054 -1.11078017535838 -1.10075679537967 -1.10515068040254 -1.09841841252615 -1.10525068092991 -1.11013377694876 -1.11442014135102 -1.12395438247066 -1.09289999828900 -1.11631092596834 -1.13869108092094 -1.13121778411954 -1.11215444772567 -1.08305854689202 -1.07883522161388 -1.07326282278712 -1.09472438786799 -1.10750902820709 -1.11217002961544 -1.13381869147951 -1.12125917557095 -1.10723556079011 -1.12557827186296 -1.11694476376681 -1.10884208834009 -1.10912360573283 -1.12847109342915 -1.11858837419542 -1.13305857893018 -1.13154828131123 -1.11008600118065 -1.11778945807900 -1.11094000460207 -1.09273674128867 -1.10301981432017 -1.07016391933250 -1.05176885156881 -1.03808129358095
and an array of Time periods for the displacement values
T = 0 0.0667334000667334 0.100100100100100 0.133466800133467 0.166833500166834 0.200200200200200 0.233566900233567 0.266933600266934 0.300300300300300 0.333667000333667 0.367033700367034 0.400400400400400 0.433767100433767 0.467133800467134 0.500500500500501 0.533867200533867 0.567233900567234 0.600600600600601 0.633967300633967 0.667334000667334 0.700700700700701 0.734067400734067 0.767434100767434 0.800800800800801 0.834167500834168 0.867534200867534 0.900900900900901 0.934267600934268 0.967634300967634 1.00100100100100 1.03436770103437 1.06773440106773 1.10110110110110 1.13446780113447 1.16783450116783 1.20120120120120 1.23456790123457 1.26793460126793 1.30130130130130 1.33466800133467 1.36803470136803 1.40140140140140 1.43476810143477 1.46813480146813 1.50150150150150 1.53486820153487 1.56823490156823 1.60160160160160 1.63496830163497 1.66833500166834 1.70170170170170 1.73506840173507 1.76843510176844 1.80180180180180 1.83516850183517 1.86853520186854 1.90190190190190 1.93526860193527 1.96863530196864 2.00200200200200 2.03536870203537 2.06873540206874 2.10210210210210 2.13546880213547 2.16883550216884 2.20220220220220 2.23556890223557 2.26893560226894 2.30230230230230 2.33566900233567 2.36903570236904 2.40240240240240 2.43576910243577 2.46913580246914 2.50250250250250 2.53586920253587 2.56923590256924 2.60260260260260 2.63596930263597 2.66933600266934 2.70270270270270 2.73606940273607 2.76943610276944 2.80280280280280 2.83616950283617 2.86953620286954 2.90290290290290 2.93626960293627 2.96963630296964 3.00300300300300 3.03636970303637 3.06973640306974 3.10310310310310 3.13646980313647 3.16983650316984 3.20320320320320 3.23656990323657 3.26993660326994 3.30330330330330 3.33667000333667 3.37003670337004 3.40340340340340 3.43677010343677 3.47013680347014 3.50350350350350 3.53687020353687 3.57023690357024 3.60360360360360 3.63697030363697 3.67033700367034 3.70370370370370 3.73707040373707 3.77043710377044 3.80380380380380 3.83717050383717 3.87053720387054 3.90390390390390 3.93727060393727 3.97063730397064 4.00400400400400 4.03737070403737 4.07073740407074 4.10410410410410 4.13747080413747 4.17083750417084 4.20420420420420 4.23757090423757 4.27093760427094 4.30430430430430 4.33767100433767 4.37103770437104 4.40440440440441 4.43777110443777 4.47113780447114 4.50450450450451 4.53787120453787 4.57123790457124 4.60460460460461 4.63797130463797 4.67133800467134 4.70470470470471 4.73807140473807 4.77143810477144 4.80480480480481 4.83817150483817 4.87153820487154 4.90490490490491 4.93827160493827 4.97163830497164 5.00500500500501 5.03837170503837 5.07173840507174 5.10510510510511 5.13847180513847 5.17183850517184 5.20520520520521 5.23857190523857 5.27193860527194 5.30530530530531 5.33867200533867 5.37203870537204 5.40540540540541 5.43877210543877 5.47213880547214 5.50550550550551 5.53887220553887 5.57223890557224 5.60560560560561 5.63897230563897 5.67233900567234 5.70570570570571 5.73907240573907 5.77243910577244 5.80580580580581 5.83917250583917 5.87253920587254 5.90590590590591 5.93927260593927 5.97263930597264 6.00600600600601 6.03937270603937 6.07273940607274 6.10610610610611 6.13947280613947 6.17283950617284 6.20620620620621 6.23957290623957 6.27293960627294 6.30630630630631 6.33967300633967 6.37303970637304 6.40640640640641 6.43977310643977 6.47313980647314 6.50650650650651 6.53987320653987 6.57323990657324 6.60660660660661 6.63997330663997 6.67334000667334 6.70670670670671 6.74007340674007 6.77344010677344 6.80680680680681 6.84017350684017 6.87354020687354 6.90690690690691 6.94027360694027 6.97364030697364 7.00700700700701
And i need to get the values of instantaneous velocity at the displacement positions.
I considered using diff and gradient, but what i would get is the average velocity.
The displacement values obtained are experimental, so there's no function I can differentiate to obtain instantaneous velocity.
Is there a way to numerically differentiate the displacement values to get instantaneous velocity, not average velocity?
