# What is the spring constant of each spring

#### rayhan619

1. The problem statement, all variables and given/known data

A compact car has a mass of 1200 kg. Assume that the car has one spring on each wheel, that the spring are identical, and that the mass is equally distributed over the four springs. draw a picture of the situation.
a) what is the spring constant of each spring if the empty car bounces up and down 2.0 times per second?
b) what will be the cars oscillation frequency while carrying four 70 kg passengers.

2. Relevant equations

f = 1/2pie(k/m)^sq root

3. The attempt at a solution

m = 1200 kg
f = 2 hz

a) k = (2*pie*f)^2 * m = (2*3.14*2hz)^2*1200 kg = 189304.32 N/m

b) m = (4*70)+1200 kg = 1480 kg

f = (1/2*pie)(189304.32 Nm^-1/1480 kg) = 1.8 hz

im not sure where I messed up.

#### Doc Al

Mentor
a) k = (2*pie*f)^2 * m = (2*3.14*2hz)^2*1200 kg = 189304.32 N/m
There are four springs, not one giant spring.

#### rayhan619

so divide k by 4?

Mentor
Yes.

#### rayhan619

so
a) k = (189304.32 N/m)/4 = 47326.08 N/m

and
b) f = (1/2*pie)(47326.08 Nm^-1/1480 kg)^sq. root = 0.9 hz

is it right?

#### Doc Al

Mentor
so
a) k = (189304.32 N/m)/4 = 47326.08 N/m
OK.

and
b) f = (1/2*pie)(47326.08 Nm^-1/1480 kg)^sq. root = 0.9 hz
No. What's the mass per spring?

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