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Undamped Spring question problem solved, but I can't plot the graph

  1. Nov 19, 2009 #1
    1. The problem statement, all variables and given/known data
    a mass weighig 2 pounds stretches a spring 6 inches. If the mass is pulled down an additional 3 inches and then released, and if there is no damping, detemine the position, u of the mass at any time, t.
    Plot u verses t.
    Find the frequency, period and amplitute of the motion


    2. Relevant equations
    solved all parts of the problem, but having trouble graphing the cosine wave


    3. The attempt at a solution
    answers: u = (1/4) cos (8t)
    R = (1/4) feet
    w (this is supposed to be the greek w, whatever that is called) = root k/m = 8 radians
    T = 2pie/w = pie / 4

    i am confused how to graph this without knowing what the phase is??
    i know that amplitute will be 1/4
    and the wave will have points at 0, pie/16, pie/8, 3pie/16 and pie/4
    but wont i need to know phase in order to know if the waveform is shifted over at all??

    ..and in order to know the phase, i would need to know the coefficient in front of second term of general solution. That is:
    u = (1/4)cos (8t) + B sin (8t)
    and
    phase = tan-1 (B/A)

    therefore i have to know what B is in order to calculate phase.

    Please tell me what im doing wrong, thanks
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 19, 2009 #2
    You get the phase from the initial conditions. In this case you've solved it correctly, so like you said, B = 0. This is equivalent with knowing the initial position and the velocity of the mass (initial velocity = 0 <=> B = 0).
     
  4. Nov 19, 2009 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    The general "wave" can be written [itex]A cos(\omega t+ \phi)[/itex] where A is the amplitude, [itex]\omega[/itex] is the frequency, and [itex]\phi[/itex] is the phase. In your example, the phase is 0.

    (And [itex]\omega[/itex] is "omega", the last letter of the Greek alphabet.)
     
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