Frequency of a Car's Vibrations?

[jumpingjack90]

Frequency of a Car's Vibrations?

Homework Statement

When four people with a combined mass of 297 kg sit down in a car, they find that the car drops 2.8 cm lower on its springs. Then they get out of the car and bounce it up and down. What is the frequency of the car's vibration if its empty mass is 2210 kg

Homework Equations

F = kx
x=k/F
f=(1/2)(pi)sqrt(m/k)
F=mg

The Attempt at a Solution

I tried using F=mg=(297)(9.8) =2910.6 N
k=103,950 N/m
f=(1/2)(pi)sqrt(2210/103950)=0.229 which was the wrong answer. Not really sure what I'm doing wrong.
Please provide solution and approach to problem. Thanks!

 

[berkeman]

Check your equation for the resonant frequency f. You have a misplaced 2 (well, actually 4):

http://hyperphysics.phy-astr.gsu.edu/hbase/shm2.html

EDIT, and the term inside the square root may be off as well...

 

[jumpingjack90]

ok. I found the equation for the frequency to be f=w/2(pi) and w=sqrt(k/m)
so, w=sqrt(103950)/297 =18.7 and f=18.7/(2)(pi) =2.97 which is also wrong. ??

 

[berkeman]

ok. I found the equation for the frequency to be f=w/2(pi) and w=sqrt(k/m)
so, w=sqrt(103950)/297 =18.7 and f=18.7/(2)(pi) =2.97 which is also wrong. ??

There are two different "m" quantities here. The first m is the mass of the people who sit in the car so that the k value can be calculated for the springs. The second m is the mass of what? What is resonating when they get out and start pushing on the car to achieve resonance?

BTW, you also had a typo in your Relevant equations when you manipulated the F=kx equation. You did the calculation correctly when you calculated k later, but x is not equal to k/F. Just a typo right there, not affecting your final math.

2. Homework Equations
F = kx
x=k/F