Vibration absorbers are used in boxcars to protect sensitive cargo from large accelerations due to periodic excitations provided by rail joints. For a particular railway, joints are spaced \(5 \mathrm{~m}\) apart. The boxcar, when empty, has a mass of \(25,000 \mathrm{~kg}\). Two absorbers, each of mass 12,000 kg, are used. Absorbers for a particular boxcar are designed to eliminate vibrations of the main mass when the boxcar is loaded with a \(12,000 \mathrm{~kg}\) cargo and travels at \(100 \mathrm{~m} / \mathrm{s}\). The natural frequency of the unloaded boxcar is \(165 \mathrm{rad} / \mathrm{s}\).

(a) At what speeds will resonance occur for the boxcar with a 12,000 kg cargo?

(b) What is the best speed for the boxcar when it is loaded with a 25,000 kg cargo?