Engineers analyze the vertical motion of a car’s wheel assembly after the car drives over a small bump. The unsprung mass associated with one wheel (tire, rim, brake hardware, and a portion of the axle) is m=45kg. The effective spring constant of the suspension acting on that mass is k=1.8×104N⋅m−1. Ignore all damping for the purposes of this calculation.
(a) Calculate the natural period of vertical oscillation of the wheel assembly.
(b) Determine the corresponding natural frequency in hertz.
(c) While cruising, the car travels at a constant speed of 30ms−1. The tire radius is 0.30m. Compute the rotational frequency of the wheel in hertz.
(d) Compare the forcing frequency found in part (c) with the natural frequency from part (b). Discuss quantitatively whether the conditions suggest a risk of resonance.
(e) To reduce the likelihood of resonance, the design team decides to increase the natural frequency by 25% while keeping the unsprung mass constant. Determine the new required spring constant.