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Homework Help: SHM Vertical

  1. May 16, 2012 #1

    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.

    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).


    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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