Dampened harmonic motion question

[sigmavirus]

Homework Statement

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).

Homework Equations

F_spring=-ky
F_drag=-bv
y(t)=y_maxe^-bt/2m

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 don't know what to do about t in the equation and i was considering using a variable (so t/2 for the 2nd oscillation)

 

[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)

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

 

[sigmavirus]

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

 

[RoyalCat]

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

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

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