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SHM Vertical

  1. May 16, 2012 #1
    SHM - VERTICAL

    Surely whether you consider the motion used to establish the SHM system, or the motion as soon as the system is released you should derive the same equation.

    DISPLACEMENT BELOW EQUILLBRIUM.
    However, consider a verticle spring with particle attached hanging in equilibrium initially, displaced downward and subject to resistance.

    -Considering intial conditions, acceleration is down => resistance is up, T is up (as spring extended), and mg down.
    - However considering the moment the system is released, acceleration is up => resistance is down, T is up, mg is down.

    The correct solution is the equation derived following the initial conditions.

    (I note that for the conditions after, I have taken T as up, but this must only hold until length l is again reached, where compression may take over depending upon the relative elastic and gpe potential models).
    (However I still do not understand why exactly conditions 2 would not mean in line to establish a valid shm equation, as some motion upward should still occur).

    DISPLACEMENT ABOVE EQUILIBIRUM:

    A system is initially in equilbrium it is the displaced in the direction upward from equilibrium - the displacement is such that the length of the spring is less than l. (for this example, l + e = 60 + 11.8cm) and displacement is 15cm.

    - This time, considering conditions after release, leads me to dervie the correct equation. The particle will accelerate downward, mg acts downward and T acts upward.
    - However, considering intial conditions, acceleration is upward, T would be downward (spring is now compressed) and mg would be downward.

    Any assitance, immensely appreciated, thank you. =]
     
  2. jcsd
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