Page 55 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

42 Free Vibration Chap. 2

Figure P2-17.

2-18 A uniform bar of length L is suspended in the horizontal position by two vertical
strings of equal length attached to the ends. If the period of oscillation in the plane of
the bar and strings is and the period of oscillation about a vertical line through the
center of gravity of the bar is ^2, show that the radius of gyration of the bar about the
center of gravity is given by the expression

2-19 A uniform bar of radius of gyration k about its center of gravity is suspended
horizontally by two vertical strings of length /i, at distances a and b from the mass
center. Prove that the bar will oscillate about the vertical line through the mass center,
and determine the frequency of oscillation.
2-20 A steel shaft 50 in. long and \\ in. in diameter is used as a torsion spring for the
wheels of a light automobile, as shown in Fig. P2-20. Determine the natural frequency
of the system if the weight of the wheel and tire assembly 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.

Figure P2-20.

2-21 Using the energy method, show that the natural period of oscillation of the fluid in a
U-tube manometer shown in Fig. P2-21 is

T = 2771

where / is the length of the fluid column.