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Homework Help: Dampened harmonic motion question

  1. Jan 7, 2010 #1
    1. The problem statement, all variables and given/known data
    Automobile of mass m=2000kg has a suspension that sags 10 cm when the entire auto is placed on it. The amp. of oscillation decreases 50% with every complete oscillation. Solve for (a) spring constant k and (b)the damping constant b for one wheel (assuming each wheel supports 500 kg).


    2. Relevant equations
    Fspring=-ky
    Fdrag=-bv
    y(t)=ymaxe-bt/2m


    3. The attempt at a solution
    I think i should use [tex]\Sigma[/tex]F=ma for the initial force, which would be gravity ant the spring. so mg=-ky then solve for k. i am not sure how correct this is, though. then for part b, i dont know what to do about t in the equation and i was considering using a variable (so t/2 for the 2nd oscillation)
     
  2. jcsd
  3. Jan 7, 2010 #2
    You need to develop the damped harmonic oscillator equation of motion. Otherwise you don't know how long one complete oscillation lasts.

    Though if you haven't studied this, I can tell you that the period of a damped oscillation, is very VERY close to that of the undamped oscillation. (I'm talking differences in the third or fourth digit here)

    [tex]\omega_{damped}\approx \omega_0=\sqrt\frac{k}{m}[/tex]
     
  4. Jan 7, 2010 #3
    i solved it using a period of 2[tex]\pi[/tex]. thanks for the help!
     
  5. Jan 8, 2010 #4
    Are you sure? Since that doesn't have the right units.

    Did you mean [tex]\frac{2\pi}{\omega}[/tex] ? If so, then you're correct. :)
     
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