The body of a 1300 Kg car is supported by four (4) springs. The people in the car have a combined mass of 300 Kg. When driven over a pothole in the road, the car vibrates with a period of 0.75 seconds in a manner that approximates simple harmonic motion. Find the spring constant of a single (1) spring.

The spring constant for a single spring is 28073.5 N/m

Explanation:

First if we assume the vibration of the approximates simple harmonic motion, the to each of the springs we can associate a natural frequency of vibration that is defined for a simple spring as:

(1)

with k the spring constant and m the mass attached to the spring

Natural frequency is related with the period (T) of the oscillation as follows:

(2)

We can equate (1) and (2):

solving for k:

(3)

k is the spring constant for a single spring, if we assume the weight of the car and the people is uniformly distributed on the four springs, then the mass m is:

Now we have all the values to put on (3):

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