An electromagnet of mass \(1500 \mathrm{~kg}\) is at rest while holding an automobile of mass \(900 \mathrm{~kg}\) in a junkyard. The electric current is turned off, and the automobile is dropped. Assuming that the crane and the supporting cable have an equivalent spring constant of \(1.75 \times 10^{6} \mathrm{~N} / \mathrm{m}\), find the following:

(a) the natural frequency of vibration of the electromagnet,

(b) the resulting motion of the electromagnet, and

(c) the maximum tension developed in the cable during the motion.