You are asked to design spring bumpers for the walls of a parking garage. A freely rolling 1300 kg car moving at 0.62 m/s is to compress the spring no more than 0.072 m before stopping. What should be the force constant of the spring? Assume that the spring has negligible mass.

Explanation:

Given:

mass of the car,

parking speed of the car,

compression of spring bumpers on the walls,

Using the equation of motion:

where:

final speed of the car

acceleration of the car while compressing the spring (will be -ve since final velocity tends to zero)

(negative sign denotes that it is reducing the speed )

Now the force:

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explanation:

resonant frequency