Question

A compact car has a mass of 1400kg. Assume that the car has one spring on each wheel, that the springs are identical, and that the mass is equally distributed over the four springs.

What is the spring constant of each spring if the empty car bounces up and down 1.9 times each second?

What will be the car's oscillation frequency while carrying four 68kg passengers?

Answer 1

The oscillation frequency is
f = [1/(2 pi)]sqrt (K/m)

K is the overall spring constant of the four springs in parallel. The k for each individual spring is K/4.

Use the first equation to solve for k and then use k = K/4.

For your second question, m increases from 1400 to 1400 + 4*68 = 1672 kg. That will multiply the original oscillation frequency by a factor sqrt(1400/1672) = 0.9151

Answer 2

I'm not sure how to solve for k though.

Answer 3

With a bit of algebra applied to the equations above.

4 pi^2 f^2 = K/m
K = 4 pi^2*m*f^2

k = K/4 = pi^2*m*f^2