# Homework Help: 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. :)