Question

The springs in a car's front suspension give it a natural frequency of 0.59 Hz. Normally, shock absorbers damp the oscillations, but this car's front shock absorbers need replacing. The car is driving on a bumpy road with bumps 37 m apart. There is a particular speed where the driver notices the car shakes violently. What is this speed?

Answer 1

The speed at which the car shakes violently is approximately 21.83 m/s.

Step-by-step explanation:

To calculate the speed at which the car shakes violently, we need to consider the natural frequency of the car's front suspension and the distance between the bumps.

The natural frequency is given as 0.59 Hz.

The wavelength (λ) of the bumps can be calculated by dividing the distance between the bumps by the number of bumps per wavelength.

The speed can then be calculated by multiplying the frequency by the wavelength.

Let's assume there is one bump per wavelength:

λ = 37 m
f = 0.59 Hz
v = f * λ = 0.59 Hz * 37 m = 21.83 m/s

Therefore, the speed at which the car shakes violently is approximately 21.83 m/s.