Page 98 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Chap. 3 Problems 85

ratio of consecutive amplitudes is 4.2 to 1.0. Determ ine the amplitude and phase when
a force F = 2 cos 3/ acts on the system.
3-4 Show that for the dampled spring-mass system, the peak amplitude occurs at a
frequency ratio given by the expression
= Vl - 2^2
3-5 A spring-mass is excited by a force sin ojt. At resonance, the amplitude is measured
to be 0.58 cm. At 0.80 resonant frequency, the amplitude is measured to be 0.46 cm.
Determine the damping factor ^ of the system.
3-6 Plot the real and imaginary parts of Eq. (3.1-17) for ^ = 0.01 and 0.02.
3-7 For the system shown in Fig. P3-7, set up the equation of motion and solve for the
steady-state amplitude and phase angle by using complex algebra.

^
X2 —2

/777777777, 7777777777777Z Figure P3-7.

3-8 Shown in Fig. P3-8 is a cylinder of mass m eonnected to a spring of stiffness k exeited
through viscous friction c to a piston with motion y = A s in a ) t . Determ ine the
amplitude of the cylinder motion and its phase with respect to the piston.

Figure P3-8.

3-9 A thin disk is supported on spring-mounted bearings with vibration pickup and
strobotac, as shown in Fig. P3-9. Running at 600 rpm ccw, the original disk indicates a
maximum amplitude of 2.80 mm at 45° cw from a reference mark on the disk. Next a