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SHM (finding the phase constant)

  1. Mar 6, 2013 #1
    1. The problem statement, all variables and given/known data

    A simple harmonic oscillator consists of a block of mass 2.00
    kg attached to a spring of spring constant 100 N/m.When t =1.00
    s, the position and velocity of the block are x = 0.129 m and v =
    3.415 m/s. (a) What is the amplitude of the oscillations? What were
    the (b) position and (c) velocity of the block at t =0 s?

    I have found a which is Xm = .500m ( I found it through the energy formula E=U+K, solve for x then Xm). But I need my phase constant to do b and c


    2. Relevant equations

    x=Xmcos (wt + Φ)


    3. The attempt at a solution

    I have found my 2 possible phase constant variable doing this

    .129 = .500cos(-7.07(1) + Φ) --> I found w using -(k/m)^1/2

    I am left with arccos .129/.500 = -7.07 + Φ

    And it's here I always get loss... 1.31 = -7.07+ Φ
    Do I need to do 2pi - 1.31 to get the second angle? If so, how do I decide which one to use?
     
  2. jcsd
  3. Mar 6, 2013 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Why do you use the minus sign?

    Find a phase constant between 0 and 2pi.

    ehild
     
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