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Conceptual Questions on a Mass Hanging from a Spring

  1. Oct 1, 2011 #1
    I don't understand what I am doing wrong.

    Answer the following questions for a mass that is hanging on a spring and oscillating up and down with simple harmonic motion. Note: the oscillation is small enough that the spring stays stretched beyond its rest length the entire time.

    Answer top/bottom/top and bottom/equilibrium/nowhere:

    1) Where in the motion is the magnitude of the force from the spring on the mass zero?
    Equilibrium, because the change in position delta x is zero.
    2) Where in the motion is the magnitude of the net force on the mass a maximum?
    The top, because the force of the spring (from compression) and the force of gravity both act on the mass.
    3) Where in the motion is the magnitude of the net force on the mass zero?
    The bottom, because the force of gravity and the force from the spring oppose each other to keep the block at rest (away from the equilibrium position)
    4) Where in the motion is the magnitude of the acceleration a maximum?
    The top, because force is maximum there.
    5) Where in the motion is the speed zero?
    It is zero at the top and bottom; it changes direction at the top and stays at rest at the bottom.
    6) Where in the motion is the acceleration zero?
    The bottom, since the net force is zero.
    7) Where in the motion is the speed a maximum?
    At equilibrium.
    8) Where in the motion is the magnitude of the force from the spring on the mass a maximum?
    The top and bottom, because of delta x.

    Yes/No

    1) When the object is at half its amplitude from equilibrium, is its speed half its maximum speed?
    x(t) = Acos(ωt + φ), cos(ωt + φ) = cos(30 deg) = .5
    v(t) = -ωAsin(ωt + φ) = (sqrt(3)/2)Aω, maximum v(t) is Aω
    No.
    2) When the object is at half its amplitude from equilibrium, is the magnitude of its acceleration at half its maximum value?
    Yes.
    a(t) = -(ω^2)Acos(ωt + φ) = .5Aω, maximum a(t) is A(ω^2)
     
  2. jcsd
  3. Oct 1, 2011 #2

    PeterO

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    Homework Helper

    true
     
  4. Oct 1, 2011 #3
    Thanks, I see what I did wrong now.
     
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