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Worksheet

Physics I: Energy Conservation Worksheet
Class: PHYS 2034 Names: Timothy Nix
Section: 001 Omar Alhallak
Lab Group: 8 Jennings Daniel
Assignment Date: 2/26/18
answer key: numbers text data
Mass of Oscillator (kg): 0.2 Stretch Distance (m) .285 Spring Constant from two points (N/m): 6.9614
Stretch Force (N) 1.984 Spring Constant from graph (N/m): 6.0646
Table 1: Force, Motion and Energy of an Oscillating Mass
time (s) force (N) position (m) velocity (m/s) kinetic energy (J) elastic energy (J) potential energy (J) total energy (J) change in energy (J)
sample# time force pos vel acc
1 1.99998 1.7326974526 -0.249361 0.7021566049 -1.3802453131
2 2.033313 1.5932457059 -0.226723 0.6447035304 -2.0351740366
3 2.066646 1.4720328797 -0.2058 0.5653839872 -2.6340068465
4 2.099979 1.3686789965 -0.1884785 0.4660559106 -3.1235062198
5 2.133312 1.2717847311 -0.1744155 0.353436451 -3.4778275423
6 2.166645 1.2049086891 -0.16464 0.2313843972 -3.7305569024
7 2.199978 1.1623512078 -0.158809 0.1014718481 -3.8808606029
8 2.233311 1.1562715676 -0.158123 -0.0248677487 -4.0455753555
9 2.266644 1.1745104881 -0.1596665 -0.1707871245 -4.0863074202
10 2.299977 1.2109883293 -0.1696135 -0.3119902032 -3.7047122883
11 2.33331 1.2900236517 -0.1816185 -0.4207508742 -3.1941322851
12 2.366643 1.3929975573 -0.1977395 -0.5213652137 -2.7326213188
13 2.399976 1.4959714629 -0.216776 -0.6049722997 -2.2101313552
14 2.433309 1.6358031872 -0.2385565 -0.6708575419 -1.6210647128
15 2.466642 1.7630956535 -0.262052 -0.7153050697 -0.9525586344
16 2.499975 1.9086270404 -0.2869195 -0.7350277669 -0.2510619657
17 2.533308 2.0606180451 -0.3116155 -0.7320264869 0.4586525758
18 2.566641 2.2243883525 -0.3363115 -0.7057295573 1.1959982254
19 2.599974 2.3638400993 -0.359464 -0.6511348447 1.8898725195
20 2.633307 2.4911325656 -0.3802155 -0.5766745167 2.4848941421
21 2.66664 2.6066457291 -0.3983945 -0.4832060821 2.9927348544
22 2.699973 2.7035399946 -0.4128005 -0.3751600016 3.4162530469
23 2.733306 2.7643363964 -0.4237765 -0.2532508658 3.7467544486
24 2.766639 2.8068938777 -0.4299505 -0.1217662177 3.9424350983
25 2.799972 2.8251327983 -0.4320085 0.0140059734 3.9811424697
26 2.833305 2.8129735179 -0.4289215 0.1472056387 3.8837189934
27 2.866638 2.7764956768 -0.4220615 0.2752602526 3.6832743596
28 2.899971 2.7096196348 -0.4103995 0.3958831255 3.3625391255
29 2.933304 2.6127253693 -0.3953075 0.5029287793 2.9130572192
30 2.966637 2.503291846 -0.3764425 0.5932530159 2.3473340992
31 2.99997 2.3699197394 -0.3551765 0.6618537019 1.6933581725
32 3.033303 2.2426272731 -0.331681 0.706729984 1.0065107551
33 3.066636 2.0723973479 -0.3074995 0.729168125 0.3046567875
34 3.099969 1.926865961 -0.2824605 0.7278818622 -0.4179205111
35 3.133302 1.7813345741 -0.258279 0.7010132601 -1.1259676581
36 3.166635 1.6418828273 -0.2351265 0.6509919266 -1.7712493137
37 3.199968 1.5142103835 -0.214375 0.5809620596 -2.3347095412
38 3.233301 1.4051568377 -0.195853 0.4922099221 -2.7928857186
39 3.266634 1.3200418751 -0.1812755 0.3911668283 -3.151732826
40 3.299967 1.23530689 -0.169785 0.284835765 -3.5621500621
41 3.3333 1.1927494087 -0.161553 0.1562094788 -4.0073443826
42 3.366633 1.1745104881 -0.158809 0.0095755124 -4.2000475422
43 3.399966 1.1805901283 -0.16121 -0.1310558939 -4.1252529908
44 3.433299 1.2231476096 -0.167384 -0.2725448088 -3.7904640033
45 3.466632 1.2778643713 -0.180075 -0.3913097464 -3.2224779909
46 3.499965 1.3686789965 -0.1943095 -0.4837777544 -2.7221405537
47 3.533298 1.4720328797 -0.212317 -0.5699573662 -2.2813529185
48 3.566631 1.5932457059 -0.2327255 -0.6395584789 -1.7439755043
49 3.599964 1.7266178124 -0.255535 -0.6887223039 -1.1235856661
50 3.633297 1.8603698965 -0.279202 -0.7158767421 -0.4442415237
51 3.66663 2.0180605638 -0.303898 -0.7188780221 0.2567787467
52 3.699963 2.1757512311 -0.3277365 -0.6984407344 0.9480328495
53 3.733296 2.3152029778 -0.3510605 -0.6549936333 1.6118940433
54 3.766629 2.4428754217 -0.3719835 -0.5895371454 2.2226368136
55 3.799962 2.5580086077 -0.3908485 -0.5050725507 2.7663265068
56 3.833295 2.6549028731 -0.406112 -0.4031719484 3.2297430668
57 3.866628 2.7339381955 -0.418117 -0.2868366184 3.5825160944
58 3.899961 2.7886549572 -0.4254915 -0.1606399397 3.8013020673
59 3.933294 2.8068938777 -0.4289215 -0.0301557182 3.8937233602
60 3.966627 2.8068938777 -0.4275495 0.1019006023 3.866092252
61 3.99996 2.7764956768 -0.4220615 0.231098561 3.7043549895
62 4.033293 2.7156992749 -0.411943 0.3525789425 3.4044621861
63 4.066626 2.63704393 -0.398223 0.4614825315 2.9770137066
64 4.099959 2.5336900469 -0.38073 0.5535217852 2.4532136474
65 4.133292 2.4063975806 -0.360836 0.6268387684 1.8586684232
66 4.166625 2.2787251367 -0.3383695 0.6785751191 1.2169597557
67 4.199958 2.1392733899 -0.3150455 0.7087308373 0.5430941952
68 4.233291 1.9755030825 -0.290521 0.715733824 -0.1611417645
69 4.266624 1.8299716956 -0.2666825 0.6981548982 -0.8649013257
70 4.299957 1.6901399713 -0.2433585 0.6568515685 -1.514470567
71 4.33329 1.5689271451 -0.222264 0.5938246882 -2.0582793598
72 4.366623 1.4477143189 -0.203399 0.5153626536 -2.4919210187
73 4.399956 1.3565197162 -0.187964 0.4314697314 -3.0078605041
74 4.433289 1.2778643713 -0.1737295 0.3192790261 -3.6033585251
75 4.466622 1.2231476096 -0.1658405 0.1817918179 -3.9190915759
76 4.499955 1.1988290489 -0.161896 0.0483063164 -3.9314779347
77 4.533288 1.1927494087 -0.1627535 -0.0818920689 -3.8367937494
78 4.566621 1.2231476096 -0.167384 -0.2086604199 -3.6733890924
79 4.599954 1.2717847311 -0.1768165 -0.3292832928 -3.4293540034
80 4.633287 1.3565197162 -0.189679 -0.4389014723 -3.1099288649
81 4.66662 1.4477143189 -0.2063145 -0.5380866309 -2.6959386407
82 4.699953 1.5628475049 -0.225694 -0.6261241779 -2.0474412958
83 4.733286 1.6901399713 -0.249018 -0.6821480715 -1.1862320579
84 4.766619 1.8238920554 -0.272342 -0.7001557516 -0.4437651253
85 4.799952 1.9694234423 -0.2958375 -0.7058724754 0.1402993338
86 4.833285 2.1271141096 -0.3198475 -0.6927240106 0.7509230045
87 4.866618 2.2665658563 -0.342657 -0.6572803228 1.3910833771
88 4.899951 2.3942383002 -0.364266 -0.5992555759 2.0108777174
89 4.933284 2.5093714862 -0.383131 -0.5210793775 2.5580212991
90 4.966617 2.6127253693 -0.3994235 -0.426467598 3.019651365
91 4.99995 2.6974603544 -0.411943 -0.3174210909 3.3881455404
92 5.033283 2.752177116 -0.420861 -0.1977986447 3.6487354743
93 5.066616 2.782575317 -0.42532 -0.0710302936 3.7891539077
94 5.099949 2.7886549572 -0.425663 0.0583105831 3.7970144816
95 5.133282 2.7643363964 -0.4213755 0.1855076884 3.6742227896
96 5.166615 2.7156992749 -0.4131435 0.3067022337 3.4216125291
97 5.199948 2.6431235702 -0.400624 0.4166062494 3.0540711506
98 5.233281 2.5519289675 -0.3850175 0.5127901279 2.5892253954
99 5.266614 2.4428754217 -0.365981 0.5915379987 2.0363650327
100 5.299947 2.3091233376 -0.345058 0.6502773361 1.4156178956
101 5.33328 2.1757512311 -0.322077 0.687436041 0.7407995381
102 5.366613 2.024140204 -0.2985815 0.7004415877 0.0393028694
103 5.399946 1.8782288395 -0.274743 0.6892939763 -0.6427805639
104 5.433279 1.7387770928 -0.252105 0.6569944866 -1.2996148811
105 5.466612 1.6114846264 -0.2303245 0.6018281016 -1.9186946237
106 5.499945 1.4959714629 -0.2114595 0.5267961013 -2.460240524
107 5.533278 1.3990771975 -0.194824 0.4360431104 -2.9302075622
108 5.566611 1.3200418751 -0.1819615 0.329569129 -3.316328479
109 5.599944 1.2474661704 -0.172529 0.2113758638 -3.570010636
110 5.633277 1.2231476096 -0.167727 0.0871800385 -3.66207463
111 5.66661 1.2109883293 -0.166698 -0.0368728687 -3.6113381986
112 5.699943 1.2292272498 -0.1702995 -0.1569240692 -3.4687759724
113 5.733276 1.2717847311 -0.177674 -0.2646843135 -3.3917185285
114 5.766609 1.3443604358 -0.187621 -0.3788758721 -3.3628964243
115 5.799942 1.4233957582 -0.20237 -0.5026429431 -2.929969363
116 5.833275 1.5385289442 -0.2224355 -0.5879650463 -2.0991305241
117 5.866608 1.6540421077 -0.2426725 -0.6375576256 -1.3534479022
118 5.899941 1.7813345741 -0.265139 -0.672429641 -0.7530667974
119 5.933274 1.926865961 -0.2879485 -0.6887223039 -0.1532811906
120 5.966607 2.0666976852 -0.3116155 -0.6845776791 0.4908094689 p f
121 5.99994 2.2183087123 -0.3342535 -0.6559940599 1.1381158178 -0.249361 1.7326974526
-0.226723 1.5932457059
-0.2058 1.4720328797
-0.1884785 1.3686789965
-0.1744155 1.2717847311
-0.16464 1.2049086891
-0.158809 1.1623512078
-0.158123 1.1562715676
-0.1596665 1.1745104881
-0.1696135 1.2109883293
-0.1816185 1.2900236517
-0.1977395 1.3929975573
-0.216776 1.4959714629
-0.2385565 1.6358031872
-0.262052 1.7630956535
-0.2869195 1.9086270404
-0.3116155 2.0606180451
-0.3363115 2.2243883525
-0.359464 2.3638400993
-0.3802155 2.4911325656
-0.3983945 2.6066457291
-0.4128005 2.7035399946
-0.4237765 2.7643363964
-0.4299505 2.8068938777
-0.4320085 2.8251327983
-0.4289215 2.8129735179
-0.4220615 2.7764956768
-0.4103995 2.7096196348
-0.3953075 2.6127253693
-0.3764425 2.503291846
-0.3551765 2.3699197394
-0.331681 2.2426272731
-0.3074995 2.0723973479
-0.2824605 1.926865961
-0.258279 1.7813345741
-0.2351265 1.6418828273
-0.214375 1.5142103835
-0.195853 1.4051568377
-0.1812755 1.3200418751
-0.169785 1.23530689
-0.161553 1.1927494087
-0.158809 1.1745104881
-0.16121 1.1805901283
-0.167384 1.2231476096
-0.180075 1.2778643713
-0.1943095 1.3686789965
-0.212317 1.4720328797
-0.2327255 1.5932457059
-0.255535 1.7266178124
-0.279202 1.8603698965
-0.303898 2.0180605638
-0.3277365 2.1757512311
-0.3510605 2.3152029778
-0.3719835 2.4428754217
-0.3908485 2.5580086077
-0.406112 2.6549028731
-0.418117 2.7339381955
-0.4254915 2.7886549572
-0.4289215 2.8068938777
-0.4275495 2.8068938777
-0.4220615 2.7764956768
-0.411943 2.7156992749
-0.398223 2.63704393
-0.38073 2.5336900469
-0.360836 2.4063975806
-0.3383695 2.2787251367
-0.3150455 2.1392733899
-0.290521 1.9755030825
-0.2666825 1.8299716956
-0.2433585 1.6901399713
-0.222264 1.5689271451
-0.203399 1.4477143189
-0.187964 1.3565197162
-0.1737295 1.2778643713
-0.1658405 1.2231476096
-0.161896 1.1988290489
-0.1627535 1.1927494087
-0.167384 1.2231476096
-0.1768165 1.2717847311
-0.189679 1.3565197162
-0.2063145 1.4477143189
-0.225694 1.5628475049
-0.249018 1.6901399713
-0.272342 1.8238920554
-0.2958375 1.9694234423
-0.3198475 2.1271141096
-0.342657 2.2665658563
-0.364266 2.3942383002
-0.383131 2.5093714862
-0.3994235 2.6127253693
-0.411943 2.6974603544
-0.420861 2.752177116
-0.42532 2.782575317
-0.425663 2.7886549572
-0.4213755 2.7643363964
-0.4131435 2.7156992749
-0.400624 2.6431235702
-0.3850175 2.5519289675
-0.365981 2.4428754217
-0.345058 2.3091233376
-0.322077 2.1757512311
-0.2985815 2.024140204
-0.274743 1.8782288395
-0.252105 1.7387770928
-0.2303245 1.6114846264
-0.2114595 1.4959714629
-0.194824 1.3990771975
-0.1819615 1.3200418751
-0.172529 1.2474661704
-0.167727 1.2231476096
-0.166698 1.2109883293
-0.1702995 1.2292272498
-0.177674 1.2717847311
-0.187621 1.3443604358
-0.20237 1.4233957582
-0.2224355 1.5385289442
-0.2426725 1.6540421077
-0.265139 1.7813345741
-0.2879485 1.926865961
-0.3116155 2.0666976852
-0.3342535 2.2183087123

f

-0.249361 -0.22672300000000001 -0.20580000000000001 -0.18847849999999999 -0.1744155 -0.16464000000000001 -0.15880900000000001 -0.15812300000000001 -0.15966649999999999 -0.1696135 -0.18161849999999999 -0.19773950000000001 -0.216776 -0.2385565 -0.26205200000000001 -0.28691949999999999 -0.31161549999999999 -0.33631149999999999 -0.35946400000000001 -0.38021549999999998 -0.39839449999999998 -0.41280050000000001 -0.4237765 -0.42995050000000001 -0.43200850000000002 -0.42892150000000001 -0.42206149999999998 -0.41039949999999997 -0.39530749999999998 -0.37644250000000001 -0.35517650000000001 -0.331681 -0.30749949999999998 -0.2824605 -0.25827899999999998 -0.23512649999999999 -0.21437500000000001 -0.195853 -0.18127550000000001 -0.16978499999999999 -0.161553 -0.15880900000000001 -0.16120999999999999 -0.16738400000000001 -0.18007500000000001 -0.1943095 -0.21231700000000001 -0.2327255 -0.25553500000000001 -0.27920200000000001 -0.303898 -0.32773649999999999 -0.3510605 -0.37198350000000002 -0.39084849999999999 -0.40611199999999997 -0.41811700000000002 -0.425491500 00000002 -0.42892150000000001 -0.42754950000000003 -0.42206149999999998 -0.411943 -0.39822299999999999 -0.38073000000000001 -0.36083599999999999 -0.33836949999999999 -0.31504549999999998 -0.29052099999999997 -0.26668249999999999 -0.24335850000000001 -0.22226399999999999 -0.203399 -0.18796399999999999 -0.17372950000000001 -0.1658405 -0.16189600000000001 -0.1627535 -0.16738400000000001 -0.17681649999999999 -0.18967899999999999 -0.20631450000000001 -0.22569400000000001 -0.24901799999999999 -0.27234199999999997 -0.29583749999999998 -0.31984750000000001 -0.34265699999999999 -0.36426599999999998 -0.383131 -0.39942349999999999 -0.411943 -0.42086099999999999 -0.42531999999999998 -0.42566300000000001 -0.42137550000000001 -0.4131435 -0.40062399999999998 -0.38501750000 000001 -0.365981 -0.34505799999999998 -0.322077 -0.2985815 -0.27474300000000001 -0.25210500000000002 -0.23032449999999999 -0.21145949999999999 -0.194824 -0.1819615 -0.17252899999999999 -0.16772699999999999 -0.16669800000000001 -0.17029949999999999 -0.177674 -0.18762100000000001 -0.20236999999999999 -0.22243550000000001 -0.24267250000000001 -0.26513900000000001 -0.2879485 -0.31161549999999999 -0.33425349999999998 1.7326974526000001 1.59324570587 1.47203287969 1.3686789965499999 1.2717847311099999 1.20490868908 1.16235120779 1.1562715675999999 1.1745104881499999 1.2109883292600001 1.2900236516600001 1.39299755729 1.49597146291 1.6358031871600001 1.7630956535 2 1.9086270404400001 2.06061804505 2.2243883525300001 2.3638400992599999 2.4911325656200001 2.6066457291299998 2.7035399945699998 2.7643363964200001 2.8068938777099999 2.8251327982599999 2.8129735178900002 2.7764956767900002 2.7096196347600001 2.6127253693100001 2.5032918459900002 2.3699197394399998 2.2426272730800001 2.07239734791 1.9268659609900001 1.78133457408 1.6418828273399999 1.51421038347 1.4051568376600001 1.32004187507 1.2353068899999999 1.1927494087099999 1.1745104881499999 1.18059012834 1.22314760963 1.27786437129 1.3686789965499999 1.47203287969 1.59324570587 1.72661781242 1.86036989648 2.0180605637600002 2.17575123105 2.3152029777799998 2.4428754216600002 2.5580086076500002 2.6549028731000002 2.7339381954899999 2.7886549571599999 2.8068938777099999 2.8068938777099999 2.7764956767900002 2.71569927494 2.6370439300499999 2.5336900469199999 2.4063975805500002 2.2787251366799999 2.13927338994 1.9755030824699999 1.8299716955500001 1.69013997131 1.56892714513 1.4477143189499999 1.35651971618 1.27786437129 1.22314760963 1.19882904889 1.1927494087099999 1.22314760963 1.2717847311099999 1.35651971618 1.4477143189499999 1.5628475049399999 1.69013997131 1.82389205537 1.9694234422900001 2.1271141095699999 2.2665658563100002 2.3942383001800001 2.5093714861800001 2.6127253693100001 2.69746035439 2.7521771160499999 2.78257531697 2.7886549571599999 2.7643363964200001 2.71569927494 2.6431235702400002 2.5519289674699999 2.4428754216600002 2.3091233376 2.17575123105 2.02414020395 1.87822883952 1.7387770927799999 1.61148462642 1.49597146291 1.39907719747 1.32004187507 1.2474661703700001 1.22314760963 1.2109883292600001 1.2292272498200001 1.2717847311099999 1.3443604358100001 1.4233957582100001 1.5385289442100001 1.65404210771 1.78133457408 1.9268659609900001 2.0666976852399999 2.2183087123399998

Conservation

Energy Conservation
Figure 1: Force and Position of Oscillating Mass over Time
Figure 2: Force of Oscillating Mass over Position, with Linear Fit
Figure 3: Energies of Oscillating Mass over Time
Figure 4: Change in Total Energy of Oscillating Mass over Time

Damping

Damping
Figure 1: Energies of Oscillating Mass over 30 seconds, with Exponential Fit
Ae^(-ct)+b
t p v acc ke pe me
0.032258 -0.317961 -0.89553668 0.868341347 0.0801985945 0.3065630966 0.3867616912
0.064516 -0.347116 -0.8759689672 1.2536152033 0.0767321632 0.3653603638 0.4420925269
0.096774 -0.375928 -0.8314136545 1.8229674549 0.0691248665 0.4285302797 0.4976551462
0.129032 -0.401653 -0.759817978 2.4481091312 0.057732336 0.489186199 0.546918535
0.16129 -0.4251485 -0.67165251 3.0691050695 0.0451117094 0.5480920064 0.5932037159
0.193548 -0.445557 -0.5622209994 3.6706058658 0.0316092452 0.6019753503 0.6335845956
0.225806 -0.462021 -0.4316711272 4.1499345623 0.0186339962 0.6472850813 0.6659190775
0.258064 -0.473683 -0.2894544678 4.4522173575 0.0083783889 0.6803740848 0.6887524737
0.290322 -0.480886 -0.139706085 4.583965349 0.001951779 0.7012234534 0.7031752324
0.32258 -0.482601 0.0087131702 4.6071102664 7.59E-06 0.7062339659 0.7062415579
0.354838 -0.4803715 0.1581661913 4.5678147747 0.0025016544 0.699723778 0.7022254324
0.387096 -0.4724825 0.308062255 4.3610365564 0.0094902353 0.6769297811 0.6864200164
0.419354 -0.4601345 0.4451100847 3.9671914505 0.0198122987 0.6420099517 0.6618222504
0.451612 -0.4433275 0.5665037441 3.4661421393 0.0320926492 0.5959660353 0.6280586845
0.48387 -0.4230905 0.6688465738 2.9203290316 0.0447355739 0.5427985935 0.5875341674
0.516128 -0.399938 0.7577504461 2.2674388884 0.0574185738 0.4850176096 0.5424361834
0.548386 -0.373527 0.8206624885 1.448719227 0.067348692 0.4230738333 0.4904225254
0.580644 -0.346087 0.8515277864 0.6081263469 0.0725099571 0.3631974063 0.4357073634
0.612902 -0.317961 0.856844297 -0.1611242328 0.0734182149 0.3065630966 0.3799813116
Figure 2: Energies of Oscillating Mass with Index Card over 30 seconds, with Exponential Fit 0.64516 -0.2903495 0.8408947651 -0.9179121647 0.0707104006 0.2556314779 0.3263418785
0.677418 -0.263081 0.7999871694 -1.720354082 0.0639979471 0.2098703728 0.2738683199
0.709676 -0.2378705 0.7283619567 -2.461627289 0.053051114 0.171574735 0.224625849
0.741934 -0.2155755 0.6359137441 -3.0360536187 0.040438629 0.1409194599 0.1813580889
0.774192 -0.196539 0.5292881697 -3.4891598868 0.0280145967 0.1171304063 0.145145003
0.80645 -0.181104 0.4096666804 -3.8770280085 0.0167826789 0.0994553731 0.116238052
0.838708 -0.169785 0.2777876806 -4.1990221344 0.0077165995 0.087411949 0.0951285486
0.870966 -0.162925 0.1360140637 -4.4099969586 0.0018499826 0.080491056 0.0823410386
0.903224 -0.160867 -0.0107807021 -4.4656973643 1.16E-05 0.0784704407 0.078482063
0.935482 -0.163611 -0.1572801062 -4.3396720172 0.0024737032 0.0811703024 0.0836440056
0.96774 -0.1713285 -0.2940325742 -4.0827888678 0.0086455155 0.0890084813 0.0976539968
0.999998 -0.182819 -0.4211857868 -3.7679162549 0.0177397467 0.1013479163 0.119087663
1.032256 -0.198597 -0.5409549569 -3.3195152723 0.0292632265 0.119596242 0.1488594686
1.064514 -0.2183195 -0.6396057653 -2.7350425223 0.0409095535 0.1445297402 0.1854392937
1.096772 -0.240443 -0.7171382121 -2.1276791947 0.0514287215 0.1753058634 0.2267345849
1.12903 -0.2649675 -0.7770966375 -1.4852169814 0.0603879184 0.2128910393 0.2732789577
1.161288 -0.2910355 -0.8168227864 -0.7255041424 0.0667199464 0.2568408505 0.3235607969
1.193546 -0.3184755 -0.8270127651 0.1242449688 0.0683950114 0.3075560129 0.3759510243
1.225804 -0.3452295 -0.806337446 0.9076114047 0.0650180077 0.3613998471 0.4264178548
1.258062 -0.3709545 -0.7652821695 1.5926755266 0.0585656799 0.4172664371 0.475832117
1.29032 -0.395136 -0.7026654887 2.2341203809 0.0493738789 0.4734404539 0.5228143328
1.322578 -0.416745 -0.621145659 2.8572527731 0.038582193 0.5266389326 0.5652211256
1.354836 -0.4357815 -0.5179167442 3.4428700519 0.0268237754 0.5758504954 0.6026742708
1.387094 -0.450702 -0.3950462762 3.884658201 0.015606156 0.6159580515 0.6315642075
1.419352 -0.4615065 -0.2616904678 4.1265353051 0.0068481901 0.6458442691 0.6526924592
1.45161 -0.4676805 -0.1249379999 4.2278896963 0.0015609504 0.6632399694 0.6648009197
1.483868 -0.469567 0.013882 4.2253462987 1.93E-05 0.6686014318 0.6686207028
1.516126 -0.46648 0.144579553 4.2584104665 0.0020903247 0.6598393672 0.6619296919
1.548384 -0.460992 0.2928511274 4.149171543 0.0085761783 0.6444050622 0.6529812405
1.580642 -0.446929 0.4225149145 3.7331988788 0.0178518853 0.6056883738 0.6235402591
1.6129 -0.4330375 0.5304696165 3.3333767887 0.0281398014 0.5686213729 0.5967611743
1.645158 -0.4131435 0.6422640206 2.7576787603 0.0412503072 0.5175758627 0.5588261699
1.677416 -0.3905055 0.7175812546 1.9284039991 0.0514922857 0.4624092104 0.5139014961
1.709674 -0.365981 0.7636576801 1.1601707784 0.0583173052 0.4061526067 0.4644699119
1.741932 -0.3407705 0.7878773396 0.5025753498 0.0620750702 0.3521244234 0.4141994937
1.77419 -0.314874 0.7971812333 -0.1715521627 0.0635497919 0.3006393117 0.3641891035
1.806448 -0.2886345 0.7803456162 -0.9335540594 0.0608939281 0.2526205327 0.3135144608
1.838706 -0.263767 0.7358936801 -1.6631276378 0.0541539508 0.2109662997 0.2651202506
1.870964 -0.2406145 0.6694372972 -2.2843524819 0.0448146295 0.1755560322 0.2203706617
1.903222 -0.220206 0.586440659 -2.8252059644 0.0343912647 0.1470382964 0.181429561
1.93548 -0.20237 0.4869037655 -3.3286715033 0.0237075277 0.1241836525 0.1478911802
1.967738 -0.188307 0.3697928507 -3.7478234145 0.0136746752 0.1075239214 0.1211985967
1.999996 -0.1781885 0.2405721061 -4.0090303397 0.0057874938 0.0962789865 0.1020664803
2.032254 -0.1727005 0.1067732552 -4.1124194489 0.0011400528 0.0904397505 0.0915798033
2.064512 -0.1713285 -0.0268779149 -4.1186507728 7.22E-05 0.0890084813 0.0890807236
2.09677 -0.1744155 -0.1606767658 -4.0409499786 0.0025817023 0.0922448907 0.094826593
2.129028 -0.18179 -0.2903405529 -3.8494321454 0.0084297637 0.1002102499 0.1086400136
2.161286 -0.1932805 -0.4133587017 -3.5031485731 0.0170865416 0.1132786975 0.1303652391
2.193544 -0.208887 -0.5205749995 -3.0124000218 0.027099833 0.1323107074 0.1594105404
2.225802 -0.227409 -0.6082974249 -2.4791767319 0.0370025757 0.1568149496 0.1938175253
2.25806 -0.2485035 -0.6800703185 -1.9352711724 0.0462495638 0.1872566224 0.2335061862
2.290318 -0.271656 -0.7353029567 -1.3187516137 0.0540670438 0.2237745895 0.2778416334
2.322576 -0.2965235 -0.7680881056 -0.6135946515 0.0589959338 0.266618574 0.3256145078
2.354834 -0.3219055 -0.7751767865 0.1078400548 0.060089905 0.3142164806 0.3743063856
2.387092 -0.347116 -0.7592272546 0.7843837949 0.0576426024 0.3653603638 0.4230029662
2.41935 -0.3712975 -0.7245222546 1.4546962111 0.0524932497 0.4180384377 0.4705316875
2.451608 -0.39445 -0.6669267227 2.151968641 0.0444791254 0.4717979904 0.5162771158
2.483866 -0.41503 -0.5837824037 2.7785346199 0.0340801895 0.5223133745 0.556393564
2.516124 -0.432523 -0.4836547868 3.268520152 0.0233921953 0.5672709961 0.5906631914
2.548382 -0.446586 -0.369497489 3.6338792056 0.0136528394 0.6047590477 0.6184118871
2.58064 -0.456533 -0.2470700636 3.9095834967 0.0061043616 0.6319991831 0.6381035448
2.612898 -0.462707 -0.1169632339 4.1382349337 0.0013680398 0.6492086614 0.6505767013
2.645156 -0.464422 0.0233335744 4.2337395106 5.44E-05 0.654030098 0.6540845436
2.677414 -0.4611635 0.1625966169 4.1169975644 0.002643766 0.6448846195 0.6475283855
2.709672 -0.4536175 0.2921127231 3.8701608352 0.0085329843 0.6239528423 0.6324858266
2.74193 -0.442127 0.4135063826 3.5440972732 0.0170987528 0.5927427364 0.6098414892
2.774188 -0.426692 0.5235286165 3.1068872396 0.0274082212 0.5520789224 0.5794871437
2.806446 -0.4079985 0.6186350845 2.5184722236 0.0382709368 0.5047650757 0.5430360124
2.838704 -0.3860465 0.6881927653 1.8452349002 0.0473609282 0.4519094309 0.4992703591
2.870962 -0.3630655 0.7361890418 1.1876394716 0.0541974305 0.3997073467 0.4539047772
2.90322 -0.338198 0.766758978 0.468493823 0.058791933 0.3468280674 0.4056200004
2.935478 -0.312816 0.768678829 -0.3092771383 0.0590867142 0.2967222289 0.3558089431
2.967736 -0.2879485 0.7454929354 -1.0476254382 0.0555759717 0.2514211491 0.3069971208
2.999994 -0.26411 0.698382744 -1.7038219982 0.0487738457 0.2115153335 0.2602891792
3.032252 -0.242501 0.6338462121 -2.2966879599 0.0401761021 0.1783196625 0.2184957646
3.06451 -0.2227785 0.5509972548 -2.8837041073 0.0303597975 0.1504938376 0.1808536351
3.096768 -0.2063145 0.4459961698 -3.3903488932 0.0198912583 0.12907189 0.1489631483
3.129026 -0.1936235 0.3265223614 -3.7125973589 0.0106616852 0.1136811082 0.1243427934
3.161284 -0.18522 0.2029134892 -3.903097833 0.0041173884 0.1040274435 0.1081448319
3.193542 -0.180418 0.074283468 -4.0392967702 0.0005518034 0.0987033503 0.0992551537
3.2258 -0.1802465 -0.0596630638 -4.0765575439 0.0003559681 0.0985157906 0.0988717587
3.258058 -0.184191 -0.1944956807 -3.9151789713 0.003782857 0.1028747937 0.1066576507
3.290316 -0.193109 -0.3185475954 -3.5446059527 0.0101472571 0.1130777597 0.1232250168
3.322574 -0.2052855 -0.4241394038 -3.1151532816 0.0179894234 0.1277876005 0.1457770239
3.354832 -0.2207205 -0.5185074676 -2.6895157067 0.0268849994 0.1477261939 0.1746111933
3.38709 -0.239071 -0.5986981696 -2.217588297 0.0358439498 0.1733109338 0.2091548836
3.419348 -0.259651 -0.6650068717 -1.6378208325 0.0442234139 0.2044335475 0.2486569615
3.451606 -0.282632 -0.7073912759 -0.96369332 0.0500402417 0.2422226936 0.2922629354
3.483864 -0.305956 -0.7255560206 -0.3183061995 0.0526431539 0.2838507949 0.3364939488
3.516122 -0.3297945 -0.7267374674 0.3041903433 0.0528147346 0.3298063272 0.3826210619
3.54838 -0.35329 -0.7085727227 0.9901446542 0.0502075303 0.3784729588 0.4286804892
3.580638 -0.376271 -0.6635300632 1.6852551963 0.0440272145 0.429312626 0.4733398404
3.612896 -0.3966795 -0.5961875952 2.2727800232 0.0355439649 0.4771464316 0.5126903964
3.645154 -0.41503 -0.5145200846 2.7730663152 0.0264730917 0.5223133745 0.5487864662
3.677412 -0.4302935 -0.4166076804 3.2221031473 0.0173561959 0.5614379141 0.57879411
3.70967 -0.4422985 -0.3043702337 3.5776701205 0.0092641239 0.5932026725 0.6024667964
3.741928 -0.4501875 -0.1819428083 3.7906796627 0.0033103186 0.6145525572 0.6178628758
3.774186 -0.454132 -0.0558233616 3.8554091296 0.0003116248 0.625369039 0.6256806638
3.806444 -0.453789 0.0704437659 3.7900438133 0.0004962324 0.6244247295 0.6249209619
3.838702 -0.44933 0.1894745317 3.6666890336 0.0035900598 0.6122136343 0.6158036941
3.87096 -0.4416125 0.3076192125 3.4836915821 0.009462958 0.5913639982 0.6008269561

Questions

Questions:

1. Within the range of noise in our measurement, does the total energy seem to be conserved during the oscillation? Looking at your graphs, do you see any evidence that some other process may have been involved in the system, interchanging energy with the others? 2. How do the graphs of energy decay compare? Has increasing the air resistance increased the rate of decay of energy from the system? 3. How does the time constant with the card compare with the time constant without the card, and how is that related to the two rates of damping?

Conclusion

Conclusion: