am doing a lab on harmonic motion on loggerpro. If you go onto logger pro in the
ID: 1645599 • Letter: A
Question
am doing a lab on harmonic motion on loggerpro. If you go onto logger pro in the top left corner there is a yellow folder the second icon, you then go to experiments --> sample data --> physics and then simple harmonic motion. There are 3 graphs position veocity and acceleration and a second page with the data.
It would not let me post a picture so this is the data below
*really need help with the last 2 questions**
Experiments>Sample Data> Physics
entitled simpleharmonicmotion.cmbl
Let’s assume these data are collected from a test configuration as shown in the earlier video we reviewed. These will be the data we will analyze and report upon. Note there are 3 sets of data (position, velocity, and acceleration) already calculated. If you want to see the raw data, change to page 2 of the LoggerPro file.
1. Analysis
Inspect the position graph and from that graph answer the following questions:
a) What is the period of the harmonic motion?
b) Select 2 full periods of motion and fit the data with an appropriate function for simple harmonic motion. Provide an image of your fit and the details of the fit parameters. What is the RMSE (root mean square error) for your fit? Is that a good fit or a poor fit?
c) From the fit parameters, what is the rest position, x0, of the oscillating mass, M?
d) What is the maximum amplitude, A, of the position oscillation?
Now consider the velocity and acceleration graphs:
e) Visually inspect the velocity graph and provide the value of the velocity when the mass is at position x0? Repeat for when the mass is at position A.
f) Visually inspect the acceleration graph and provide the value of the acceleration when the mass is at position x0? (be sure you are consistent with proper use of signs for positive and negative directions) Repeat for when the mass is at position A.
g) Now from the curve fit parameters provided from b) above, write the equations for the velocity and acceleration of the mass, as a function of time.
h) The harmonic motion is governed by a single parameter of the system, that is the ratio of the spring constant (k) to the mass (M), i.e. k/M. Using the data you have collected so far, provide the best fit value for k/M.
time position Velocity Acceleration 00.0333333
0.0666667
0.1
0.133333
0.166667
0.2
0.233333
0.266667
0.3
0.333333
0.366667
0.4
0.433333
0.466667
0.5
0.533333
0.566667
0.6
0.633333
0.666667
0.7
0.733333
0.766667
0.8
0.833333
0.866667
0.9
0.933333
0.966667
1
1.03333
1.06667
1.1
1.13333
1.16667
1.2
1.23333
1.26667
1.3
1.33333
1.36667
1.4
1.43333
1.46667
1.5
1.53333
1.56667
1.6
1.63333
1.66667
1.7
1.73333
1.76667
1.8
1.83333
1.86667
1.9
1.93333
1.96667
2 0.562755
0.568414
0.573388
0.577332
0.580076
0.581105
0.580419
0.578018
0.574245
0.569272
0.563612
0.557952
0.552464
0.547834
0.544404
0.542346
0.542517
0.543889
0.546977
0.551264
0.556409
0.56224
0.567899
0.573044
0.57716
0.580076
0.581276
0.580762
0.578532
0.574931
0.570129
0.564812
0.558981
0.553493
0.54852
0.544918
0.542689
0.542174
0.543375
0.546119
0.550235
0.55538
0.56104
0.566699
0.572015
0.576303
0.57939
0.58059
0.580419
0.578704
0.575274
0.570643
0.565327
0.559839
0.554523
0.549206
0.545433
0.543032
0.542346
0.543203
0.546119 0.162345058303
0.149988764255
0.128537538114
0.0966076886311
0.0538782082459
0.00500165702049
-0.0444468253068
-0.0896073424326
-0.126906443737
-0.153208879993
-0.164505544967
-0.16207221594
-0.146343852092
-0.117043961956
-0.0777465230366
-0.0285875922142
0.0208632915524
0.0657490551551
0.106621212815
0.137768927662
0.158920552498
0.16577808951
0.156917224546
0.13476976419
0.101617860194
0.0590257272217
0.0101474828501
-0.0393018081565
-0.0843200418104
-0.121477069772
-0.147496996889
-0.162211328852
-0.16392256436
-0.151064526576
-0.123905302811
-0.0850335209395
-0.039588915113
0.00957648449391
0.0571698256691
0.0997609948471
0.134055131389
0.156351401276
0.164501601068
0.158913025634
0.138910878917
0.106192962182
0.0631655843852
0.0164355975439
-0.0291525668339
-0.0751728590912
-0.11547792055
-0.143350102989
-0.157486412339
-0.159487288549
-0.152497155589
-0.129340975218
-0.0906092792806
-0.0451648984774
-8.94595069563E-005
0.0394436066338
0.0677534312346 -0.463944395275
-0.608264741738
-0.828868756654
-1.0947413947
-1.31916654027
-1.41584247155
-1.36971443566
-1.19595783837
-0.91638492364
-0.548071546133
-0.137932179206
0.267591137209
0.658462825525
1.00266381956
1.27128941937
1.40736548386
1.38078588427
1.25629609593
1.04726727344
0.755694574976
0.393325264726
-0.0266924416026
-0.441437699702
-0.805602289893
-1.10590839247
-1.32223547407
-1.4158377735
-1.36736397054
-1.19479054409
-0.926162474578
-0.597660179441
-0.230142636003
0.172946715438
0.583017752082
0.949206187169
1.21819751702
1.37133246114
1.40261914106
1.31162508127
1.1136918388
0.817190092398
0.444338424178
0.0367128387561
-0.376394675315
-0.765323585337
-1.08570075833
-1.28838726666
-1.35776807162
-1.3416711253
-1.2307586846
-0.978748803952
-0.628657890103
-0.258713338684
0.0931651174971
0.475125439161
0.881113113382
1.17809352301
1.28444905825
1.22753920058
1.08314901023
0.952084548016 mall mass spring and and dowrn tor. Try hed on the phs. Notice ps between city vs 0.57. 0.56 0.55 Time: 0.07 s Position: 0.573 m 0.0 2.0 Statistics for: Latest I F osition min:0.5422 at 1.233 max: 0.5813 at 0.8667 Auto Fit for Latest | Position vs time u can also ed on the aphing You can do me label e graph ition" Can XA'cos(Bt+CHD mean: 0 5620 median: 0.5628 0.1 Time: 0.07 s Velocity: 0.1285 m/s 2 0.0 0.1 it for Latest | Velocity Linear F v = mt+D uto Fit for Latest 1 Velocity 0.5 14m(Slope):-001702miss I A 0.1640+0.0006827 b (Y-Intercept): 0.007935ms B: 8.8920.006980 · (At 2.00 Av0.000) orrelation:-0.08670 C: 0077520.008301 D:-0.0004222 +-0.0004896 Correlation: 0.9995 RMSE: 0.003711 m/s RMSE: 0.1148 m/s Av: 0.3303 Integral for Latest| Velocity Integral:-0.01851 m/s s Time:0.07 s Acceleration: -0.8289 m/s Linear Fit for Late sti Acceleration 0 2.0 m (Slope) 0.3889 m/s's b (Y-intercept) (At 2.00 y 0 00) | Integral for -0 43 11 m/s, Time (s) Integral: - Correlation: 0.2256 RMSE: 0.9859 m/s 3:00 PM
Explanation / Answer
As you have asked only last two parts so in part h)
Since, acceleration =(K/M) *position
So if you plot the graph between acceleration and position so it will be a straight line and ita slope will be K/M which is the best fit value. Please plot graph using excel if you are having problem then let me know.
Part i) here as we obtain K/M from part h and Mass is given so spring constant can be found out.
Also total energy = 1/2 k*x^2 +1/2 M*v^2
Here position and velocity can be taken at any particular time take it at t=0.
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