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SHM: Equation relating acceleration and displacement

  1. Mar 24, 2015 #1
    A particle moves such that its acceleration is given by: a = -β(x-2). Here β is a positive constant and c is the distance from origin What is the time period of oscillation for the particle?

    Solution: a = 0 at x = 2 (mean position)
    a = -βX where X = x-2.
    So, ω2 = β ⇒ T = 2π/ω = 2π/√β

    My question is, why do we need to substitute x-2 as X? Can't we solve the problem without doing this?
     
  2. jcsd
  3. Mar 24, 2015 #2

    BruceW

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    you can do the whole problem without the substitution. I guess that using the substitution means that you can immediately recognise that the problem is SHM.
     
  4. Mar 24, 2015 #3
    So then, would we call x-2 as the distance from the mean position or x?
     
  5. Mar 24, 2015 #4
    There's not much depth involved in this. I am overthinking things.
     
  6. Mar 25, 2015 #5

    BruceW

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    yeah :) x-2 is the displacement from the equilibrium position, which makes it a convenient choice to use as coordinate, instead of using x.
     
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