Page 53 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Free Vibration Chap. 2
40

Figure P2-11.

2-12 A chronograph is to be operated by a 2-s pendulum of length L shown in Fig. P2-12. A
platinum wire attached to the bob completes the electric timing circuit through a drop
of mercury as it swings through the lowest point, (a) What should be the length L of
the pendulum? (b) If the platinum wire is in contact with the mercury for 0.3175 cm of
the swing, what must be the amplitude 6 to limit the duration of contact to 0.01 s?
(Assume that the velocity during contact is constant and that the amplitude of
oscillation is small.)

5.08 cm
\y /À Figure P2-12.

2-13 A hydrometer float, shown in Fig. P2-13, is used to measure the speeific gravity of
liquids. The mass of the float is 0.0372 kg, and the diameter of the cylindrical section
protruding above the surface is 0.0064 m. Determine the period of vibration when the
float is allowed to bob up and down in a fluid of specific gravity 1.20.

Figure P2-13.

2-14 A spherical buoy 3 ft in diameter is weighted to float half out of water, as shown in
Fig. P2-14. The center of gravity of the buoy is 8 in. below its geometric center, and the