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Homework Help: Find how far apart are the particles from each other

  1. Nov 16, 2014 #1
    1. The problem statement, all variables and given/known data
    Two particles oscillate in simple harmonic motion with amplitude A, about the centre of a common straight line of length 2A. Each particle has a period of 3.3 s, and their phase constants differ by π/9 rad. (Assume the lagging particle starts at +A. Also assume that the +x-axis is to the right. Use any variable or symbol stated above as necessary.)
    I want to find how far apart are the particles from each other (in terms of A) 0.50 s after the lagging particle leaves one end of the path?

    2. Relevant equations
    x(t) = Acos(wt + ϕ)
    w= sqrt(k/m)
    x(0) = Acos( ϕ)

    3. The attempt at a solution
    1. I found that w = 1.9
    2. the phase constant for the lagging particle is 2pi or 0 since A=Acos(phase constant)
    3. i used the equation for displacement and found that x = 0.58A for the lagging particle
    4. the phase constant for the first particle is pi/9 for the second particle since we're told their phase constants differ by this much
    Now my question is how do i find the displacement of the leading particle? Can i just use the same time (t value) as the lagging particle?
    I already tried just using the same equation for the leading particle as i did for the lagging particle and only replacing ϕ with pi/9 instead of 0. But, i got the wrong answer
    ie. lagging = x(0.5) = Acos(1.9(0.5) + 0) = 0.58m
    x(0.5) = Acos(1.9(0.5) + pi/9) = 0.27
    0.58-0.27= 0.31m
  2. jcsd
  3. Nov 16, 2014 #2

    Simon Bridge

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    Science Advisor
    Homework Helper

    ... if particle 1 lags particle 2 by ##\delta## then ##\phi_2-\phi_1=\cdots## what?
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