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Simple harmonic oscillator

  1. Jun 15, 2012 #1
    1. The problem statement, all variables and given/known data

    A physical system is designed having the following equation of motion

    md2x/dt2 + c(dx/dt) - kx = 0.

    (a) From the corresponding subsidiary equation, find the solution to this equation of motion. (HINT: use the solution of the damped harmonic oscillator as a guide).
    (b) How many distinct types of solution and hence physical behaviour does it exhibit ( does it have solutions that correspond to underdamping, overdamping, critical damping?)

    2. Relevant equations



    3. The attempt at a solution

    From the hint, I expect the solutions to the system to be similar to the damped solution.

    So the damped solution was x = -β +- √ (β2 - ω2 )

    β = c/m and ω2 = k/m

    So now I am stuck! Anyone care to point me in the right direction?
    Thanks!
     
  2. jcsd
  3. Jun 15, 2012 #2

    rock.freak667

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    Homework Helper

    Hint: x=e^rt is a solution of that equation (so substitute it into the DE and see what you get).
     
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