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Question about mg on oscilations course

  1. Oct 3, 2015 #1
    On a test our teacher asked about a system composed of (string -> mass -> string -> mass) hanging, that began to oscillate up and down.
    We all considered weight (mg) when applying Newton's second law to find the associated differential equation.
    When we met our teacher again he said that we shouldn't have, the weight has no dynamic effect on the system, because the weight force is not variable over time (as opposed to a simple or double pendulum, there it depends of the angle).
    Should i NOT include weight on the sum of forces if said weight doesn't depend on the angle?
    This was supposed to be a normal mode exercise but since it was hanging, we all encountered a forced oscillation (forced by mg)
    Please help x.x
  2. jcsd
  3. Oct 3, 2015 #2
    What makes the system to oscillate? Are these strings elastic?
  4. Oct 3, 2015 #3
    Damn, i actually meant spring, yes they are elastic, of course, didn't mean string :D
  5. Oct 4, 2015 #4
    If you first do the simpler problem of one spring + mass hanging from a ceiling, you will find that the weight only changes the equilibrium position of the mass. You can stretch or compress the spring from that equilibrium position, and it will oscillate with the same frequency depending on the spring constant and the mass. The differential equation for oscillations about equilibrium is still the same. This is what your teacher meant when he said the weight has no dynamic effect. The same thing happens if you have a two spring - two mass system
  6. Oct 4, 2015 #5


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    Why would including the weight force in your equation of motion affect the period of the oscillation? But would there also not be a mean force from the spring, balancing the weight?
  7. Oct 4, 2015 #6
    At this stage, instead of wondering why something would and something else would not happen, we should actually write down the equation of motion, and see how the different features happen. This is done, in every introductory book on calculus based physics, for the single spring + mass program. Once you work that out, you will find that extending it to the two-spring + two-mass problem is not difficult. To answer your last questions in anticipation of your working it out, the weight indeed does not effect the period of oscillation, and yes, there would be a stretch in the spring to balance the weight. That stretch would be the equilibrium position, and oscillations occur about that equilibrium position.
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