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Spring Oscillation Problem

  1. Jan 18, 2008 #1
    [SOLVED] Spring Oscillation Problem!!!

    1. A 2.0 kg mass hangs at rest from a harmonic spring with a spring constant of 500 N/m inside an elevator that is stationary.
    a) by how much is the spring stretched
    b) suppose that the elevator is rising with a constant upward accel of 1/3 g. By how much is the spring stretched now.
    c) The elevator stops at t=0. You observe that the mass starts to oscillate. What are the ampliturde A, frequency f, and the phase phi of the oscillation.




    2. F=ma=kx-mg, phi= inverse tan[ wx(o)/v(0)].



    3. I think i got a and b but am confused with c.
    a) F=kx-mg.
    mg=kx = (2)(9,8)= (500)x
    x= 0.039 m
    b) ma=kx-mg
    (2)(9.8/3)=(500x)-2(9,8)
    x=0.052 m.
    c) w= sqrt(k/M)= 16.58 rad/sec
    x(0)=0.052-0.039=0.01306. I think this is x(0) but what is v(o)?
     
  2. jcsd
  3. Jan 18, 2008 #2

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    OK.

    OK.

    A = 0.052-0.039=0.01306. (Edited.)

    You can find v0 from x0, m, k etc, or not? Any other idea comes to mind?
     
    Last edited: Jan 18, 2008
  4. Jan 18, 2008 #3
    after thinking about it, i think its easier than i thought. we calculated w. To find the amplitude of the oscillation we take the answer in b and subtract it from a. The phase is then easy to calculate since x(o)=Asin(phi) and if x(o)=amplitude, then sin(phi)=1 and the phase is pi/2
     
  5. Jan 18, 2008 #4

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    I have edited the answer for (c), because I misunderstood the meaning of x(0). The amplitude in (c) is 0.052-0.039=0.01306.

    The rest you know.
     
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