Page 101 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

88 Harmonically Excited Vibration Chap. 3

Figure P3-22.

3-23 Derive Eqs. (3.5-8) and (3.5-9) for the amplitude and phase by letting y = F sin cor
and X = X sin (cor - (f>) in the differential equation (3.5-1).
3-24 An aircraft radio weighing 106.75 N is to be isolated from engine vibrations ranging in
frequencies from 1600 to 2200 cpm. W hat statical deflection must the isolators have
for 85% isolation?
3-25 A refrigerator unit weighing 65 lb is to be supported by three springs of stiffness k
Ib/in. each. If the unit operates at 580 rpm, what should be the value of the spring
constant k if only 10% of the shaking force of the unit is to be transmitted to the
supporting structure?
3-26 An industrial machine of mass 453.4 kg is supported on springs with a static deflection
of 0.508 cm. If the machine has a rotating unbalance of 0.2303 kg • m, determine (a)
the force transmitted to the floor at 1200 rpm and (b) the dynamic amplitude at this
speed. (Assume damping to be negligible.)
3-27 If the machine of Prob. 3-26 is mounted on a large concrete block of mass 1136 kg and
the stiffness of the springs or pads under the block is increased so that the statical
deflection is still 0.508 cm, what will be the dynamic amplitude?
3-28 An electric motor of mass 68 kg is mounted on an isolator block of mass 1200 kg and
the natural frequency of the total assembly is 160 cpm with a damping factor of
= 0.10 (see Fig. P3-28). If there is an unbalance in the motor that results in a
harmonic force oi F = 100 sin 31.4i, determine the amplitude of vibration of the block
and the force transmitted to the floor.

Figure P3-28.
3-29 A sensitive instrument with mass 113 kg is to be installed at a location where the
acceleration is 15.24 cm /s^ at a frequency of 20 Hz. It is proposed to mount the