Page 139 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

126 Transient Vibration Chap. 4

4-22 If the natural period r of the oscillator is large compared to that of pulse duration ij,
the maximum peak response will occur in the region t > ty For the undamped
oscillator, the integrals written as
sin w„t('f{i)cos (oj di - cos (o„t f f{^) sin (ojd^
•'o •'0
do not change for I > i„ because in this region fit) = 0. Thus, by making the
substitution
Acoscj) = 0)^ r '/ ( i ) cos (oj
•'o
A sin 4) = r'f( i) sin ojJ
•'o
the response for t > is a simple harmonic motion with amplitude A, Discuss the
nature of the response spectrum for this case.
4-23 Derive Eqs. (4.5-4) and (4.5-5) for the half-sine pulse, and verify the primary and the
residual SRS curves of Fig. 4.5-5. (Note that n = 2 ior t^/r > 1.5 in the primary SRS
equation.)
4-24 The base of an undamped spring-mass system, m and k, is given a velocity pulse, as
shown in Fig. P4-24. Show that if the peak occurs at i < ij, the response spectrum is

Figure P4-24.