Modified Atwood Machine

Dr. A. C. Baroudy acbaroudy@gmail.com

Abstract The following is a detailed study of the motion of an unconventional Atwood Machine where one mass is constrained to move along a fixed vertical axis. The differences with the regular Atwood Machine are : 1- the tension T on the string on either side of the pulley though it is the same, however it is not constant in the present case because of the obliquity of the 2d part of the string. 2- the unique and constant acceleration (a) in the simple machine is replaced in here with two different and variable accelerations whose ratio is however constant. 3- In the simple machine the constant acceleration makes plotting and animation of the system a straightforward procedure according to 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. However in the modified Atwood machine that we present in here the accelerations being variable there is no way to get the displacement as a direct function of time. This seems to make plotting & animation an impossible task. However we were able to devise a trick to overcome this difficulty.

The following is a modified Atwood Machine where the heavier mass m2 is constrained to move along a fixed vertical axis as seen in Figure-1 below.

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At t = 0 the lighter mass m1 is at position x = 0 corresponding to O origin of the x-axis with the positive being upward while mass m2 is initially held in place at a distance 10 meters above the level of m1. The string attached to m1 & m2 passes over a small pulley of insignificant mass with no friction such that the distance of the Fixed Axis to the pulley is (d) meters. Hence the total length of the string is constant and equal to (10 + d) meters. At t = t we let go on m2 which is allowed to drop downward in the direction of (-x) while m1 moves upward by (h) meters which its abscissa LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JJW1yb3dHRiQ2JS1GLDYlUSNtMUYnRi9GMkYvRjIvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw== from origin O i.e. 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 . When m1 reaches this height, m2 will have dropped from from B to C such that AC = h + d. From right angle triangle ABC we get the total drop of m2 as BC: 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, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEjQkNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSJ+RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkwtRjY2LVEiPUYnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yNzc3Nzc4ZW1GJy9GTkZTRjUtSSZtc3FydEdGJDYjLUYjNiotSSVtc3VwR0YkNiUtRiw2JlEiaEYnRi8vJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnRjItRiM2JS1JI21uR0YkNiVRIjJGJ0ZqbkY5Ri9GMi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRjY2LlEiK0YnRmpuRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZqb0Zfby1GNjYuRjhGam5GOUY7Rj5GQEZCRkRGRkZIRkpGTS1GLDYmUSJkRidGL0ZqbkYyRlxwRmduRjkvJStleGVjdXRhYmxlR0Y9Rjk=, and its abscissa LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JJW1yb3dHRiQ2JS1GLDYlUSNtMkYnRi9GMkYvRjIvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw== from origin O is 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 . Since 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 then the relation between the abscissa of m1 & m2 along x-axis is: 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. (1) From the above relation between the abscissa of m1 & m2 we can get the relation between velocities of m1 & m2 by taking the derivative with respect to time of (1): 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. (2) From this last relation between the velocities we can see that 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 , because 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. Note that 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 = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiZRIjFGJy8lJWJvbGRHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjctRiM2KC1JI21pR0YkNidRJGNvc0YnRjIvJSdpdGFsaWNHUSZmYWxzZUYnRjVGOC1JKG1mZW5jZWRHRiQ2Ji1GIzYnLUY9NidRJyYjOTUyO0YnRjJGQEY1RjhGMi9GQUY0L0Y2USxib2xkLWl0YWxpY0YnRjhGMkY1RjhGMkZLRkxGOC8lLmxpbmV0aGlja25lc3NHRjEvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGUi8lKWJldmVsbGVkR0ZCRjIvJStleGVjdXRhYmxlR0ZCRjVGOA== hence we have: 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. Therefore, for a given \316\270, we can take the derivative relative to time of the above to get a similar relation between the accelerations: \316\2631 & \316\2632: 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 \342\206\222 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. (2.1) Note: Ernest Mach in his "La Mecanique, French Edition, 1904, p:324 " arrived at the same relation between accelerations as stated above by using a different approch than ours, his method was based on D'Alembert Principle of virtual work. Getting The Velocities Of m1 & m2 At Any Value Of h Now to get the value of these velocities for any height h of m1 we equate the change in the Potential Energy (PE) of the system at any time with the change in its Kinetic Energy (KE) since the system, as describe above, is a conservative one. If we consider the zero PE at the origin O then 1- initially at t = 0 the system has PE = 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 & no KE. 2- at t = t when m1 has moved upward by h meters and m2 downward by 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 meters then the new PE of the system is : 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, hence the change in PE is: 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 while the total KE is: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JS1GLzYkUSIyRidGMi8lJ2l0YWxpY0dRJXRydWVGJy9GM1EnaXRhbGljRicvJS5saW5ldGhpY2tuZXNzR0YxLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkMvJSliZXZlbGxlZEdRJmZhbHNlRictSSNtb0dGJDYtUScmc2RvdDtGJ0YyLyUmZmVuY2VHRkgvJSpzZXBhcmF0b3JHRkgvJSlzdHJldGNoeUdGSC8lKnN5bW1ldHJpY0dGSC8lKGxhcmdlb3BHRkgvJS5tb3ZhYmxlbGltaXRzR0ZILyUnYWNjZW50R0ZILyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGZ24tSSNtaUdGJDYlUSNtMUYnRjpGPUZJLUklbXN1cEdGJDYlLUZbbzYlUSN2MUYnRjpGPS1GIzYmLUZKNi1RIn5GJ0YyRk1GT0ZRRlNGVUZXRllGZW5GaG5GN0Y6Rj0vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUZKNi1RIitGJ0YyRk1GT0ZRRlNGVUZXRlkvRmZuUSwwLjIyMjIyMjJlbUYnL0ZpbkZgcEYrRkktRltvNiVRI20yRidGOkY9RkktRl9vNiUtRltvNiVRI3YyRidGOkY9RmRvRmlvLyUrZXhlY3V0YWJsZUdGSEYy = 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, where in this last equation we replaced v2 by its value as function of v1 found above in (2). 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 (3) which once solved for v1 gives : 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. (4) Our problem has the fallowing data: m1 = 1kg, m2 = 5kg, d = 3m, distance from the pulley to m1 = 10m, g = 9.8m/s^2. We find that when m1 gets to the pulley i.e. when h = 10m its speed = 12.88981m/s, with acceleration \316\2631 = LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlEsNi40NTcyMDMwMDFGJy8lJWJvbGRHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjE=m/s^2 . Its free fall from 10m would give it v =14m/s. As for m2 at t time it will be 12.64911m below the level of the pulley and its speed = 13.24738m/s, with acceleration \316\2632 = LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlEsNi42MzYzMTQ0ODdGJy8lJWJvbGRHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjE=m/s^2. Getting the Time of Ascension of m1 When h = 10m And m2 at 12.64911m Below Pulley Level To get the time of fall of m2 from 12.64911m height & that of the ascension of m1 when h = 10m, which must be the same, we need to find first the acceleration of m1 & m2 at that moment when sin(\316\270) = 3/13 corresponding to \316\270 = LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEoMC4yMzI4NkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw== radian then we use the following equations of motion: 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 \342\206\222 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, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYxLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RJyZzZG90O0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZMLUYsNiVRJGNvc0YnL0YwRj1GOS1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJyYjOTUyO0YnRlJGOS8lK2V4ZWN1dGFibGVHRj1GOUY5LUY2Ni1RKCZtaW51cztGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GW28tRiw2JVEjbTJGJ0YvRjJGNS1GLDYlUSJnRidGL0YyLUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjc3Nzc3OGVtRicvRk5GZ28tRjY2LVEqJnVtaW51czA7RidGOUY7Rj5GQEZCRkRGRkZIRmpuRlxvRl1vRjUtRiw2JVEoJiM5NDc7MkYnRi9GMkZlbkY5 \342\206\222 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 (5) with equation (2.1) as 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 Once equations of motion are solved for \316\2631 & \316\2632 then we use the following equation 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 \342\206\222 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 , to get the time of ascension of m1 & the time of fall of m2. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LlEhRicvJStmb3JlZ3JvdW5kR1EqWzI1NSwwLDBdRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y3LyUpc3RyZXRjaHlHRjcvJSpzeW1tZXRyaWNHRjcvJShsYXJnZW9wR0Y3LyUubW92YWJsZWxpbWl0c0dGNy8lJ2FjY2VudEdGNy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkY= We get : 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 = LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEsNi42MzYzMTQ0ODdGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=, where \316\2632 is in fact LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtbkdGJDYkUSw2LjYzNjMxNDQ4N0YnRi9GLw== since it is in the direction of (-x). and 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 = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JFEsNi40NTcyMDMwMDFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0Yn, where \316\2631 is positive since it is in the direction of (+x). as for the time we have: 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 = LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEsMS45OTYxOTA5MjBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic= , 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 = LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEsMS45OTYxOTUzMzJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic= . As we expected the time for m1 to reach the pulley and the time for m2 to get at 12.64911m below the level of the pulley is exactly the same: t \342\211\210 2seconds. Note about problem getting displacements as function of time Note that here there is no straightforward approach to get the displacement s of m1 or m2 as a direct function of time t as is the case in a conventional Atwood machine where, once the common and CONSTANT acceleration a of either mass is found from the equations of motion we get the known relation: 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 that we can plot for equal increment of time intervals then proceed to the animation. Here either acceleration \316\2631 or \316\2632 is function of time through angle \316\270 which is function of time. Unfortunately there is no way to get \316\270 as function of time in the present case. The other way around this difficulty is to start with equation 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, then integrate from x = 0 to x = h for 0 \342\211\244 h \342\211\244 10 to get the time t when m1 is at height x = h. However for plotting purpose this is not helpful at all since what we need is to start with a given time then deduce from it the corresponding height. On the other hand even if the expression above is of some help for our purpose, its integration is not possible even numerically! To be able to get a correct and more realistic plotting we still need the displacements at equal time intervals. The way around this difficulty is explained in the followings: Our way of getting the displacements of m1 & m2 along with the corresponding time To get an animation of the system we need the time of descent of m2 which is also that of the ascent of m1. We solved our problem above, however we could not get the coordinates of m1 & m2 as function of time directly. The best we could do is to get the time as we did by : 1- getting 1st angle \316\270 for a given h, 2- getting the speed v1 of m1, 2- solving equations of motion to get \316\2631 or \316\2632 knowing their relation in equation (2.1) 3- finally getting the time as t = v/\316\263. Using a for.. to.. loop with a great number of cycles ( i = 320) we get a list L of the abscissas of m1 & m2 with the corresponding time. In this list L we just extract the smallest interval of time which is found to be around 0.3 second then we take 0.3 as a unit of time and choose from the list L all multiples of 0.3. With 320 loops we found only 7 multiples of 0.3 since the total time is very short around 2 seconds as we found above. With these 7 intervals of 0.3 second and its multiples we pick from the list the corresponding abscissas of m1 & m2 and make a new list LL with only 7 entries that we plot. With these data we were able to get the animation of the system .

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC8lK2V4ZWN1dGFibGVHRj1GOQ==

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

KiYpIiIjIyIiIkYkRiYpKiYsJiooSSNtMkc2IkYmSSJnR0YsRiYpLCYqKEYkRiZJImRHRixGJkkiaEdGLEYmRiYqJClGMkYkRiZGJkYlRiZGJiooSSNtMUdGLEYmRi1GJkYyRiYhIiJGJiwmRjZGJiooRitGJiksJkYyRiZGMUYmRiRGJkYvRjdGJkY3RiVGJg==

LCQqKikiIiMjIiIiRiVGJykqJiwmKihJI20yRzYiRidJImdHRi1GJyksJiooRiVGJ0kiZEdGLUYnSSJoR0YtRidGJyokKUYzRiVGJ0YnRiZGJ0YnKihJI20xR0YtRidGLkYnRjNGJyEiIkYnLCZGN0YnKihGLEYnKSwmRjNGJ0YyRidGJUYnRjBGOEYnRjhGJkYnRjxGJ0YvRjhGOA==

At h = 2 m

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

JCIjKSohIiI=

IiIk

IiIi

IiIm

IiIj

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

KiYpIiIjIyIiIkYkRiYpLCYqJiQiKylvJEdnYiEiKkYmKSIjO0YlRiZGJiQiK3ZNNkNBRiwhIiJGJUYm

JCIrWmdDRmohIio=

LCQqKiMiIiYiIzsiIiIpIiIjI0YnRilGJyksJiomJCIrKW8kR2diISIqRicpRiZGKkYnRickIit2TTZDQUYwISIiRipGJ0YxRidGNA==

JCErZnYwNHohIio=

JCIrW3VQYSkpISIq

Note that m1 in free fall from 10m acquires v = sqrt(2*g*10) = -14m/s Here it gets v = 12.88m/s. While m2 in free fall from 12.649 will acquire v = -15.74m/s. Here it gets v = -13.2473m/s

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

IiM1

KiYpIiIjIyIiIkYkRiYpLCYqJiQiK0RdKjQheSEiKkYmKSIkZyJGJUYmRiYkIiswISo+ZzohIikhIiJGJUYm

JCIrXjkpKilHIiEiKQ==

LCQqKiMiIzgiJGciIiIiKSIiIyNGJ0YpRicpLCYqJiQiK0RdKjQheSEiKkYnKUYmRipGJ0YnJCIrMCEqPmc6ISIpISIiRipGJ0YxRidGNQ==

JCErMCJRWksiISIp

LCQqJiQiK1t1UGEpKSEiKiIiIikiIzUjRiciIiVGJ0Yn

JCIrNWRidTohIik=

Forming our list L with 320 entries and list LL with only 7 entries We then form our reduced list LL with only 7 time intervals of 0.3 second and its multiples 1*0.3 = 0.3s , 2*0.3 = 0.6s , 3*0.3 = 0.9s , 4*0.3 = 1.2s , 5*0.3 = 1.5s , 6*0.3 = 1.8s , 7*0.3 = 2s we then pick from list L the corresponding abscissas of m1 & m2 and make a new list LL with only 7 entries that we plot. With these data we were able to get the animation of the system .

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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LlEhRicvJStmb3JlZ3JvdW5kR1EqWzI1NSwwLDBdRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y3LyUpc3RyZXRjaHlHRjcvJSpzeW1tZXRyaWNHRjcvJShsYXJnZW9wR0Y3LyUubW92YWJsZWxpbWl0c0dGNy8lJ2FjY2VudEdGNy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkY= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LlEhRicvJStmb3JlZ3JvdW5kR1EqWzI1NSwwLDBdRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y3LyUpc3RyZXRjaHlHRjcvJSpzeW1tZXRyaWNHRjcvJShsYXJnZW9wR0Y3LyUubW92YWJsZWxpbWl0c0dGNy8lJ2FjY2VudEdGNy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkY=

NyI=

This is the list where the time interval and m1, m2 abscissas are recorded. The first smallest interval of time is about 0.3s as we see from the first entry: 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. The last entry is: 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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC8lK2V4ZWN1dGFibGVHRj1GOQ==

The reduced list LL with only 7 entries ready for plotting.

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