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Springs in a car (damped harmonic oscillator)

  1. Sep 25, 2012 #1
    This is a problem I've been trying to solve for quite some time now. Any help would be appreciated.

    1. The problem statement, all variables and given/known data
    When a person with the mass of 105kg sits in a car, the body of the car descends by 2,5cm in total. In the car there are four shock absorbers filled with oil and a spring around each of them. The mass of an empty car is 1250kg. When the car drives over a bump in the road, the body of the car starts oscillating vertically at the frequency of 0,85Hz.

    a) Determine the spring constant of each spring
    b) Determine the viscosity of the oil, when it is assumed that the viscosity is 1/10000 of the value of the damping constant b (-kx - bv = ma).
    c) How much does the amplitude of the vibration of the car body decrease during one oscillation? Hint: Calculate the ratio of the amplitudes of two consecutive oscillations.


    2. Relevant equations
    http://en.wikipedia.org/wiki/Harmonic_oscillator#Damped_harmonic_oscillator


    3. The attempt at a solution
    The first one I think I can solve
    a)
    m = (1250kg+105kg)/4 = 338,75kg
    x = 2,5cm = 0,025m
    g = 9,81m/s^2

    k = F/x = mg/x = (338,75kg*9,81m/s^2)/0.025m = 132925,5N/m

    However, after that no matter what I try, I'm not really getting anywhere. I always end up in a situation where I feel some information is missing when trying to solve for the damping constant.
     
  2. jcsd
  3. Sep 26, 2012 #2

    Simon Bridge

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    Define: M=unoccupied mass of car, m=mass of occupants.

    If you want to use (M+m)g=keffx ... then x needs to be the total amount the springs are compressed from having no car on them. You don't have that figure.

    for b and c I need to see what you are trying.
     
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