Ruler Data


This data models the harmonic motion of the vibrating rulers in the movies.


40 cm   equilibrium  
    0.0817  
Time(s) y(m) adjusted y(m) Theory y(m)
0 -0.0634 0.01829 0.01829
0.004 -0.0902 -0.00854 -0.00636253
0.008 -0.1171 -0.0354 -0.03040741
0.012 -0.1398 -0.0581 -0.05154826
0.016 -0.1553 -0.0736 -0.06776603
0.02 -0.1634 -0.0817 -0.07751185
0.024 -0.1634 -0.0817 -0.07985497
0.028 -0.1545 -0.0728 -0.0745716
0.032 -0.139 -0.0573 -0.06216633
0.036 -0.1163 -0.0346 -0.04382391
0.04 -0.0911 -0.00935 -0.02129612
0.044 -0.065 0.01666 0.003265542
0.048 -0.0415 0.04024 0.027515327
0.052 -0.0228 0.05894 0.049137283
0.056 -0.0089 0.072757 0.066066419
0.06 0 0.0817 0.076685934
0.064 0 0.0817 0.079981617
0.068 -0.0057 0.076009 0.075638718
0.072 -0.0187 0.063 0.064072001
0.076 -0.035 0.04674 0.046386137
0.08 -0.0561 0.0256 0.024270201
0.084 -0.0813 0.0004 -0.00016364
0.088 -0.1065 -0.0248 -0.02458186
0.092 -0.1285 -0.0468 -0.0466524
0.096 -0.1455 -0.0638 -0.06426744
0.1 -0.1561 -0.0744 -0.07574467
0.104 -0.1577 -0.076 -0.07998796
0.108 -0.1528 -0.0711 -0.07659207
0.112 -0.1406 -0.0589 -0.06588131
0.116 -0.1219 -0.0402 -0.0488786
0.12 -0.0992 -0.01748 -0.02720778
0.124 -0.074 0.00772 -0.0029385
0.128 -0.0512 0.03048 0.021611412
0.132 -0.0317 0.04999 0.044097347
0.136 -0.0179 0.06381 0.062371799
0.14 -0.0081 0.07357 0.07468948
0.144 -0.0049 0.076822 0.079874001
0.148 -0.0081 0.07357 0.077430216
0.152 -0.0179 0.06381 0.067591518
0.156 -0.0325 0.04918 0.051297544
0.16 -0.0512 0.03048 0.030104438
0.164 -0.0732 0.00853 0.006036231
0.168 -0.0968 -0.01505 -0.01860846
0.172 -0.1187 -0.037 -0.04147597
0.176 -0.1366 -0.0549 -0.06038234
0.18 -0.1488 -0.0671 -0.07352195
0.184 -0.1537 -0.072 -0.0796399
0.188 -0.1504 -0.0687 -0.0781519
0.192 -0.1423 -0.0606 -0.06920007



30 cm   equilibrium  
    0.020625  
Time(s) y(m) adjusted y(m) Theory y(m)
0 -0.03938 -0.018755 -0.01876
0.004 -0.04125 -0.020625 -0.02095053
0.008 -0.035 -0.014375 -0.01729174
0.012 -0.02375 -0.003125 -0.00880515
0.016 -0.01313 0.007495 0.002139808
0.02 -0.00563 0.015 0.012487341
0.024 -0.00125 0.019375 0.019348448
0.028 0 0.020625 0.020807529
0.032 -0.00375 0.016875 0.016457214
0.036 -0.01 0.010625 0.007512097
0.04 -0.02 0.000625 -0.00353037
0.044 -0.03 -0.009375 -0.01358718
0.048 -0.03813 -0.017505 -0.01985048
0.052 -0.03938 -0.018755 -0.02057159
0.056 -0.0325 -0.011875 -0.01554918
0.06 -0.0225 -0.001875 -0.00618549
0.064 -0.01125 0.009375 0.004905173
0.068 -0.005 0.015625 0.014626327
0.072 -0.00125 0.019375 0.020263857
0.076 -0.00063 0.02 0.020243782
0.08 -0.005 0.015625 0.014571707
0.084 -0.01188 0.008745 0.004831257
0.088 -0.02188 -0.001255 -0.00625806
0.092 -0.03188 -0.011255 -0.01560015
0.096 -0.03875 -0.018125 -0.02058673
0.1 -0.03813 -0.017505 -0.01982556
0.104 -0.03 -0.009375 -0.01352915
0.108 -0.02 0.000625 -0.00345545
0.112 -0.01125 0.009375 0.007583005
0.116 -0.00438 0.01625 0.016504306
0.12 -0.00188 0.01875 0.020817657
0.124 -0.0025 0.018125 0.019318784
0.128 -0.00688 0.01375 0.012426167
0.132 -0.01438 0.006245 0.002064204
0.136 -0.02375 -0.003125 -0.00887408
0.14 -0.0325 -0.011875 -0.01733475
0.144 -0.03875 -0.018125 -0.02095561
0.148 -0.03688 -0.016255 -0.01872573
0.152 -0.0275 -0.006875 -0.01126769
0.156 -0.01938 0.001245 -0.00066374
0.16 -0.01 0.010625 0.010125518
0.164 -0.005 0.015625 0.018087765
0.168 -0.0025 0.018125 0.020999966
0.172 -0.00375 0.016875 0.018049042
0.176 -0.00938 0.01125 0.010058883
0.18 -0.01688 0.003745 -0.00073968
0.184 -0.02563 -0.005005 -0.01133173
0.188 -0.035 -0.014375 -0.01876
0.192 -0.0375 -0.016875 -0.02095053



20 cm   equilibrium  
    0.03713  
Time(s) y(m) adjusted y(m) Theory y(m)
0 -0.00396 0.03317 0.031
0.002 0 0.03713 0.034888319
0.004 -0.00693 0.030199 0.028019317
0.006 -0.02079 0.01634 0.012510954
0.008 -0.04208 -0.00495 -0.006854985
0.01 -0.06089 -0.02376 -0.024107285
0.012 -0.07426 -0.03713 -0.033926445
0.014 -0.07376 -0.03663 -0.033284865
0.016 -0.06287 -0.02574 -0.022380366
0.018 -0.04406 -0.00693 -0.004575197
0.02 -0.02327 0.01386 0.014640669
0.022 -0.00891 0.028219 0.029342291
0.024 -0.00297 0.03416 0.034996633
0.026 -0.00446 0.032675 0.029860257
0.028 -0.01832 0.01881 0.015516892
0.03 -0.03515 0.00198 -0.003610887
0.032 -0.05594 -0.01881 -0.0216253
0.034 -0.0698 -0.03267 -0.032971857
0.036 -0.07228 -0.03515 -0.034152008
0.038 -0.06436 -0.02723 -0.024801869
0.04 -0.04604 -0.00891 -0.007804423
0.042 -0.02822 0.00891 0.011599406
0.044 -0.01287 0.02426 0.027426722
0.046 -0.00644 0.030694 0.034797395
0.048 -0.00594 0.031189 0.031438783
0.05 -0.01634 0.02079 0.018386466
0.052 -0.03069 0.00644 -0.000335058
0.054 -0.05099 -0.01386 -0.018953272
0.056 -0.06436 -0.02723 -0.031727512
0.058 -0.07129 -0.03416 -0.034719022
0.06 -0.06485 -0.02772 -0.027005411
0.062 -0.05099 -0.01386 -0.010965064
0.064 -0.03267 0.00446 0.008456206
0.066 -0.01584 0.02129 0.025270125
0.068 -0.00891 0.028219 0.034292357
0.07 -0.00693 0.030199 0.032741025
0.072 -0.01386 0.02327 0.02109446
0.074 -0.02822 0.00891 0.002943716
0.076 -0.04554 -0.00841 -0.016114681
0.078 -0.0604 -0.02327 -0.030204344
0.08 -0.06931 -0.03218 -0.034980924
0.082 -0.06535 -0.02822 -0.02897163
0.084 -0.05198 -0.01485 -0.014029343
0.086 -0.03614 0.00099 0.005238694
0.088 -0.0198 0.01733 0.022891453
0.09 -0.01188 0.02525 0.033485956
0.092 -0.00842 0.028714 0.033755537
0.094 -0.01386 0.02327 0.023617075
0.096 -0.02723 0.0099 0.006196621


40 cm Ruler

40 cm: y(t) = 0.08*SIN(2*PI()/(0.162/2)*t-ASIN(0.01829/0.08)+PI())


30 cm Ruler

30 cm: y(t) = 0.021*SIN(2*PI()/(0.141/3)*t-ASIN(-0.01876/0.021)+PI())


20 cm Ruler

20 cm: y(t) = 0.035*SIN(2*PI()/(0.067/3)*t+ASIN(0.031/0.035))