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Apparently, the equations of motion of this system should result in SHM if the small-angle approximation is used. However, I get an angular velocity term in the theta equation.. what am I not seeing?
![Name: 2016-05-02 18.36.46.jpg
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You'll have to rotate it; it's not behaving.
You'll have to rotate it; it's not behaving.
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#2
(Original post by StarvingAutist)
Apparently, the equations of motion of this system should result in SHM if the small-angle approximation is used. However, I get an angular velocity term in the theta equation.. what am I not seeing?
![Name: 2016-05-02 18.36.46.jpg
Views: 645
Size: 172.0 KB]()
You'll have to rotate it; it's not behaving.
Apparently, the equations of motion of this system should result in SHM if the small-angle approximation is used. However, I get an angular velocity term in the theta equation.. what am I not seeing?
You'll have to rotate it; it's not behaving.
Can you not just change reference frame to where it's stationary and then show it's SHM there, and then in the moving frame it will have a translation added on top of that?
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(Original post by lerjj)
Is the whole thing simply moving to the right at constant velocity?
Can you not just change reference frame to where it's stationary and then show it's SHM there, and then in the moving frame it will have a translation added on top of that?
Is the whole thing simply moving to the right at constant velocity?
Can you not just change reference frame to where it's stationary and then show it's SHM there, and then in the moving frame it will have a translation added on top of that?
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#4
(Original post by StarvingAutist)
No, the support also performs SHM; it moves in the opposite direction to the pendulum and starts doing so when the pendulum is released. I don't think I could change to the CoM frame because the CoM velocity wouldn't be constant.
No, the support also performs SHM; it moves in the opposite direction to the pendulum and starts doing so when the pendulum is released. I don't think I could change to the CoM frame because the CoM velocity wouldn't be constant.
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(Original post by lerjj)
Okay, sorry, couldn't read the question clearly due to the rotation thing. So basically, you have a pendulum and the thing it's hanging from is oscillating horizontally?
Okay, sorry, couldn't read the question clearly due to the rotation thing. So basically, you have a pendulum and the thing it's hanging from is oscillating horizontally?
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#6
(Original post by StarvingAutist)
Apparently, the equations of motion of this system should result in SHM if the small-angle approximation is used. However, I get an angular velocity term in the theta equation.. what am I not seeing?
![Name: 2016-05-02 18.36.46.jpg
Views: 645
Size: 172.0 KB]()
You'll have to rotate it; it's not behaving.
Apparently, the equations of motion of this system should result in SHM if the small-angle approximation is used. However, I get an angular velocity term in the theta equation.. what am I not seeing?
You'll have to rotate it; it's not behaving.
If you imagine the pendulum hanging vertically at rest, and then given an impulse to the right by someone inside the trolley, then by conservation of momentum, the trolley must move to the left in such a way as to keep the c-o-m of the system stationary. You then need to check that SHM for small pendulum angles => SHM for the c-o-m of the trolley.
Or is that too simple? Maybe I've misunderstood the problem.
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#7
(Original post by StarvingAutist)
Apparently, the equations of motion of this system should result in SHM if the small-angle approximation is used. However, I get an angular velocity term in the theta equation.. what am I not seeing?
![Name: 2016-05-02 18.36.46.jpg
Views: 645
Size: 172.0 KB]()
You'll have to rotate it; it's not behaving.
Apparently, the equations of motion of this system should result in SHM if the small-angle approximation is used. However, I get an angular velocity term in the theta equation.. what am I not seeing?
You'll have to rotate it; it's not behaving.
(Original post by atsruser)
I'm afraid I don't have the time to look at this at the moment, but you have taken a Lagrangian approach for some reason. However, it would seem to be more straightforward to consider conservation of momentum.
If you imagine the pendulum hanging vertically at rest, and then given an impulse to the right by someone inside the trolley, then by conservation of momentum, the trolley must move to the left in such a way as to keep the c-o-m of the system stationary. You then need to check that SHM for small pendulum angles => SHM for the c-o-m of the trolley.
Or is that too simple? Maybe I've misunderstood the problem.
I'm afraid I don't have the time to look at this at the moment, but you have taken a Lagrangian approach for some reason. However, it would seem to be more straightforward to consider conservation of momentum.
If you imagine the pendulum hanging vertically at rest, and then given an impulse to the right by someone inside the trolley, then by conservation of momentum, the trolley must move to the left in such a way as to keep the c-o-m of the system stationary. You then need to check that SHM for small pendulum angles => SHM for the c-o-m of the trolley.
Or is that too simple? Maybe I've misunderstood the problem.
Should clear things up a little bit.
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#8
(Original post by StarvingAutist)
Apparently, the equations of motion of this system should result in SHM if the small-angle approximation is used. However, I get an angular velocity term in the theta equation.. what am I not seeing?
![Name: 2016-05-02 18.36.46.jpg
Views: 645
Size: 172.0 KB]()
You'll have to rotate it; it's not behaving.
Apparently, the equations of motion of this system should result in SHM if the small-angle approximation is used. However, I get an angular velocity term in the theta equation.. what am I not seeing?
You'll have to rotate it; it's not behaving.
0
reply
Report
#9
(Original post by atsruser)
I'm afraid I don't have the time to look at this at the moment, but you have taken a Lagrangian approach for some reason. However, it would seem to be more straightforward to consider conservation of momentum.
If you imagine the pendulum hanging vertically at rest, and then given an impulse to the right by someone inside the trolley, then by conservation of momentum, the trolley must move to the left in such a way as to keep the c-o-m of the system stationary. You then need to check that SHM for small pendulum angles => SHM for the c-o-m of the trolley.
Or is that too simple? Maybe I've misunderstood the problem.
I'm afraid I don't have the time to look at this at the moment, but you have taken a Lagrangian approach for some reason. However, it would seem to be more straightforward to consider conservation of momentum.
If you imagine the pendulum hanging vertically at rest, and then given an impulse to the right by someone inside the trolley, then by conservation of momentum, the trolley must move to the left in such a way as to keep the c-o-m of the system stationary. You then need to check that SHM for small pendulum angles => SHM for the c-o-m of the trolley.
Or is that too simple? Maybe I've misunderstood the problem.
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#10
(Original post by lerjj)
Pendulums aren't closed systems though since they're subject to gravity. Doesn't that rule out a conservation of momentum argument?
Pendulums aren't closed systems though since they're subject to gravity. Doesn't that rule out a conservation of momentum argument?
But I think that it's best just to slog it out with the full Lagrangian approach for this problem.
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