Measuring Automobile Spring Constant

## Question:

When four people with a combined mass of 181 kg sit down in a
car, they find that the car drops 1.1 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 mass (when empty)
is 2500 kg? Answer in units of HZ.
## Answer:

Assuming the car has no shock absorbers it would be possible to
predict the frequency of its vibration using Hookes law. If you
try this experiment with a real car you will get way different
results. Hookes law says the force provided by a spring is
proportional to the displacement from the spring's neutral
position. In a formula it looks like this:
F=k*x where F is force, x is displacement and k is the
spring constant.
We can determine k by taking the empty car sitting on its
springs as the neutral position. The weight of the four people
then compresses the car's springs .011 meters. The weight of
the people is their mass 181kg times the acceleration due to
gravity of 9.8 meter per second per second, or 1773.8 Newtons. In
our formula, plugging the 1733.8 in for F and .011 in for x, we
get k=1773.8/.011 or
k=161255Newtons per meter.

The frequency of vibration of mass on a spring is given by the
formula frequency equals the square root of k/m, divided by 2pi.
That will be your answer in hertz.

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