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Switching between distance variables in a simple seismograph

  1. May 1, 2015 #1
    Below is an example problem from my textbook. I don't fathom the highlighted portion where they replace the y variable with x in accordance with fig. 3.6.3?

    Please help

    Thanks

    image.jpg image.jpg
     
  2. jcsd
  3. May 1, 2015 #2
    Doesn't figure 3.2.5 explain it?
     
  4. May 1, 2015 #3
    Here is the other Figure. Unfortunately, I still don't fathom??


    image.jpg
     
  5. May 2, 2015 #4
    In figure 3.2.5 they are simply substituting in X'e to simplify the equation. From Newton's 2nd law of motion:
    ∑F = m⋅d2X/dt2
    m⋅d2X/dt2 = mg - k(X - Xe) .........(Eq. 1)

    At equilibrium we know that ∑F = 0, therefore:
    mg - k(X - Xe) = 0
    → X - Xe = mg / k ...............(Eq. 2)

    Making the following two substitutions into (Eq. 1):
    Xe = X'e - mg/k
    X = X'e + x
    → m⋅d2(X'e + x)/dt2 = mg - k((X'e + x) - (X'e - mg/k))
    → m⋅d2(x)/dt2 = mg - kx + mg
    → m⋅d2x/dt2 = kx .........(Eq. 3)

    Now Eq.3 is simpler than Eq. 1, agreed?

    I assume your textbook already has all this.
     
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