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(Solved): The suspension system of a car traveling on a bumpy road has a stiffness of k=5106N/m and the e ...
The suspension system of a car traveling on a bumpy road has a stiffness of and the effective mass of the car on the suspension is . The road bumps can be considered to be periodic half-sine, . Determine the displacement response of the car. Assume the damping of the system to be negligible.
Expert Answer
To determine the displacement response of the car, we can use the concept of resonance, which occurs when the frequency of the forcing function matches the natural frequency of the system. The natural frequency of the system is given by: The forcing function can be written as a sum of its Fourier series components: The displacement response of the car can be written as: where X is the amplitude of the displacement and ? is the phase angle.The amplitude of the displacement can be found using the following formula:Continuing the next step.