A steel shaft 50 in. long and 1.5 in. in diameter is used as a torsion spring for the wheels of a light automobile, as shown below. Determine the natural frequency of the system if the weight of the wheel and tire assemble is 38 lb and its radius of gyration about its axle is 9.0 in. Discuss the difference in the natural frequency with the wheel locked and unlocked to the arm. (Ans. fn = 6.60 cps (locked wheel); fn = 7.05 cps (unlocked)) 24" -38 lb.