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Differential equation for a vibration problem

  1. May 29, 2016 #1
    1. The problem statement, all variables and given/known data
    The data given was the acceleration of the component over time, as below:
    time | Acceleration (m/s²)
    0 | 0
    0,2 |3,61
    0,4 |4,5
    0,6 |5,4
    0,8 |7,508
    1 |12

    -
    The Rigidity constat is 12600000 [N/m] (for the spring)
    The damping constant is 6500 [N/m] (for the damp)

    The system has 2 of each.
    2. Relevant equations
    1. I was required to construct the 3rd degree equation
    2. Generate the differential equation
    3. Determine the oscilation
    4. Solve the equation knowing that y(0)=0 and y'(0)=0 (So i get Constant1 and Constant2)
    5. Generate graphics for y(t) from 0 < t < 3s
    3. The attempt at a solution
    For nº 1 i got the following:
    f(t) = 3600 * (33,697*x^3 - 46,4018*x^2 + 24,693*x + 0,0615)

    For nº 2:
    Knoginw that, C=6500 * 2 = 13000 and K=12600000 *2 = 25200000

    So,
    3600*y''+13000*y'+25200000*y= 121309,2*x^3- 167043,6*x^2 + 88834,3*x + 221,4

    for the particular solution i used:
    A*x^3 + B*x^2 + C*x + D

    got the info of A,B,C and D and replaced.

    Got the following:
    y(t) = e^-1,8*t * [C1*cos(83,647*t)+C2*sen(83,647*t)]+ 4,81*(10^-3) * t^3 - 6,64*(10^-3) * t^2 + 3,523*(10^-3) * t +1,57*10^-5

    And the problem goes on...

    What i need \/
    The point is, I'd like to port all this info to Matlab or Geogebra or whatever software you recommend, but i have no idea on how to, would be anyone able to help ?

    I'd like to get the A,B,C and D, plus C1 and C2 and them generate the graphs, all on the software, using the data given.
     
  2. jcsd
  3. May 30, 2016 #2

    Simon Bridge

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