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Oscillation, Frequency, Amplitude etc Hmwk Problem

  1. Jan 25, 2010 #1
    1. The problem statement, all variables and given/known data

    A 200g mass attached to a horrizontal spring oscillates at a frequency of 2.0 Hz. At one instant, the mass is at x=5.0cm and has vx = -30cm/s.

    A. Determine the period. T= ____seconds

    B. Determine the amplitude. A =____cm

    C. Determine the maximum speed. vmax = ____ cm/s

    D. Determine the total energy. ____ J

    2. Relevant equations

    A. T = 1/frequency

    B. ????

    C. vmax= 2(pi)(f)(A) = 2piA/T

    D. ????

    Others: deltaL = mg/k where k=spring constant



    3. The attempt at a solution

    A. Answer = 0.5 seconds from T = 1/f.... T = 1/(2.0Hz).... T=0.5 secods

    B.

    C. vmax=2pi(2.0Hz)(A)

    D.


    I'm not looking for just the answers; I am in desperate need of an explanation of HOW to do the problem. Any help is greatly appreciated!!!
     
  2. jcsd
  3. Jan 26, 2010 #2

    kuruman

    User Avatar
    Homework Helper
    Gold Member

    Mechanical energy is conserved. What is the mechanical energy when the mass is at x=5.0 cm and has vx = -30 cm/s? That's the answer to part D.

    What is an expression for the mechanical energy when the particle is at maximum displacement, i.e. when x = A? Write an equation and solve for A. This will give you the answer to part B.
     
  4. Jan 26, 2010 #3
    Thank you,
    I was able out to figure out the problem last night by following a post on yahoo. I want to post it step by step here for other stumped students:

    Part B. Determine the amplitude.
    w = 2(pi)f
    w = 2(pi)(2.0Hz)
    w = 12.6 rad/sec

    v = w Sqrt(A2-x2)
    -0.30 = (12.6rad/sec) Sqrt[ (A2) - (0.502m) ]
    -0.0238 = Sqrt[ (A2) - 0.25 ]
    -0.02382 = A2 - 0.25
    -5.6644x10-4 = A2 - 0.25
    0.2494 = A2
    Sqrt (0.2494) = A
    A = 0.4994m --> 5.0 cm
    ****** However, the correct answer from Mastering Physics is 5.5cm, where did I mess up?
    A = 5.5 cm

    Part C. Determine the maximum speed.
    vmax = wA
    vmax = (12.6rad/s)(0.055m)
    vmax = 0.69m --> 70 cm

    Part D. Determine the total energy.
    Etotal = (mvmax2) / 2
    Etotal = (0.2kg)(0.72m) / 2
    Etotal = 0.049 J
     
  5. Jan 26, 2010 #4

    kuruman

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    Homework Helper
    Gold Member

    When you square both sides, the left side must be positive.
     
  6. Jan 26, 2010 #5
    Oh! thank you so much kuruman!!!
     
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