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Cars have shock absorbers to damp the oscillations that would otherwise occur when the springs that attach the wheels to the car's frame are compressed or stretched. Ideally, the shock absorbers provide critical damping. If the shock absorbers fail, they provide less damping, resulting in an underdamped motion. You can perform a simple test of your shock absorbers by pushing down on one corner of your car and then quickly releasing it. If this results in an up-and-down oscillation of the car, you know that your shock absorbers need changing. The spring on each wheel of a car has a spring constant of 6005 N/m, and the car has a mass of 1191 kg, equally distributed over all four wheels. Its shock absorbers have gone bad and provide only 49.7% of the damping they were initially designed to provide. What will the period of the underdamped oscillation of this car be if the pushing-down shock absorber test is performed?
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