GR9277 #7



Alternate Solutions 
sharpstones 20061201 09:33:27  At the least you should be able to figure out the modes. In one case all are moving together as a single mass so there is no frequency (they give you this one). In another case the two pendulums move in the same direction and the tube M moves in the opposite direction. In the last case the two pendulums move opposite directions and the tube stands still.  Clearly the last case which you are trying to find will be independent of M so (A) is the only answer the works.  

Comments 
Yaroslav Shustrov 20170904 10:47:25  I do not understand the following point. When we are speaking about certain normal mode we imply that every degree of freedom of the system oscillates with the same frequency. We can see that for 2 eigenfrequences proposed in the problem. \r\n However when I imagine that M stands still, while two pendulums oscillate with the same frequency in the opposite directions I arrive to the contradiction. In this case frequency of M is different, it equals zero. How come?   bass 20140716 06:11:28  ???????????????????????????????????????????????????????????????????????????????????????????
BASS http://www.livingscriptures.com/jpshoes.asp?cheap=productsc181.html   explainthatagain 20061212 10:44:45  Ok, can someone explain that to me again. For some reason saying A is an obvious choice doesn't work for me. How would someone know the formula to find the eigenfrequencies from. Does it follow the logic that you can go with neither pendulum is moving, they are moving in oposite directions, or they are moving in the same direction?
Poop Loops 20081005 13:00:23 
That is exactly it. 0 is when there is no oscillation, the big formula is when both masses are moving in the same direction, but since the tube can move, it has to move opposite to conserve momentum, and you are looking for the one where both masses are moving in opposite directions.

spacemanERAU 20091022 09:10:12 
well...like EVERY ETS question...this question is not designed for the test taker to "solve". I mean if you want you can set up the differential equations and solve them but good luck finishing the PGRE in 180 minutes.

keradeek 20111003 03:24:37 
study the chapter on coupled oscillations in marion and thornton and it will become obvious to you, too.

speiro 20120912 23:56:11 
marion 12.18 helped..

  sharpstones 20061201 09:33:27  At the least you should be able to figure out the modes. In one case all are moving together as a single mass so there is no frequency (they give you this one). In another case the two pendulums move in the same direction and the tube M moves in the opposite direction. In the last case the two pendulums move opposite directions and the tube stands still.  Clearly the last case which you are trying to find will be independent of M so (A) is the only answer the works.   kokorets 20060103 15:33:57    kokorets 20060103 15:33:32 
minaesm 20091005 04:29:43 
What I try and work till now is that I use limits: in the frequency which is given in the question think of this : What if the M is really bigger than two smaller m s? it's the answer . It goes to answer A.
It also works in similar questions.

 

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