• Support PF! Buy your school textbooks, materials and every day products Here!

Springs in a car (damped harmonic oscillator)

  • Thread starter harr
  • Start date
  • #1
1
0
This is a problem I've been trying to solve for quite some time now. Any help would be appreciated.

Homework Statement


When a person with the mass of 105kg sits in a car, the body of the car descends by 2,5cm in total. In the car there are four shock absorbers filled with oil and a spring around each of them. The mass of an empty car is 1250kg. When the car drives over a bump in the road, the body of the car starts oscillating vertically at the frequency of 0,85Hz.

a) Determine the spring constant of each spring
b) Determine the viscosity of the oil, when it is assumed that the viscosity is 1/10000 of the value of the damping constant b (-kx - bv = ma).
c) How much does the amplitude of the vibration of the car body decrease during one oscillation? Hint: Calculate the ratio of the amplitudes of two consecutive oscillations.


Homework Equations


http://en.wikipedia.org/wiki/Harmonic_oscillator#Damped_harmonic_oscillator


The Attempt at a Solution


The first one I think I can solve
a)
m = (1250kg+105kg)/4 = 338,75kg
x = 2,5cm = 0,025m
g = 9,81m/s^2

k = F/x = mg/x = (338,75kg*9,81m/s^2)/0.025m = 132925,5N/m

However, after that no matter what I try, I'm not really getting anywhere. I always end up in a situation where I feel some information is missing when trying to solve for the damping constant.
 

Answers and Replies

  • #2
Simon Bridge
Science Advisor
Homework Helper
17,841
1,642
Define: M=unoccupied mass of car, m=mass of occupants.

If you want to use (M+m)g=keffx ... then x needs to be the total amount the springs are compressed from having no car on them. You don't have that figure.

for b and c I need to see what you are trying.
 

Related Threads for: Springs in a car (damped harmonic oscillator)

  • Last Post
Replies
1
Views
1K
Replies
4
Views
1K
Replies
3
Views
659
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
540
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
3
Views
17K
Top