Page 58 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Chap. 2 Problems 45

Figure P2-30.

2-31 Determine the effective mass moment of inertia for shaft 1 in the system shown in Fig.
P2-31.

I

1 / Fi' Figure P2-31.

2-32 Determine the kinetic energy of the system shown in Fig. P2-32 in terms of i.
Determine the stiffness at and write the expression for the natural frequency.

Figure P2-32.

2-33 Tachometers are a reed-type frequency-measuring instrument consisting of small
cantilever beams with weights attached at the ends. When the frequency of vibration
corresponds to the natural frequency of one of the reeds, it will vibrate, thereby
indicating the frequency. How large a weight must be placed on the end of a reed
made of spring steel 0.1016 cm thick, 0.635 cm wide, and 8.890 cm long for a natural
frequency of 20 cps?
2-34 A mass of 0.907 kg is attached to the end of a spring with a stiffness of 7.0 N/cm.
Determine the critical damping coefficient.
2-35 To calibrate a dashpot, the velocity of the plunger was measured when a given force
was applied to it. If a ^-Ib weight produced a constant velocity of 1.20 in./s, determine
the damping factor Í when used with the system of Prob. 2-34.