Dampened harmonic motion question

1. Jan 7, 2010

sigmavirus

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 $$\Sigma$$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. Jan 7, 2010

RoyalCat

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)

$$\omega_{damped}\approx \omega_0=\sqrt\frac{k}{m}$$

3. Jan 7, 2010

sigmavirus

i solved it using a period of 2$$\pi$$. thanks for the help!

4. Jan 8, 2010

RoyalCat

Are you sure? Since that doesn't have the right units.

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