Page 138 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Chap. 4 Problems 125

4-17 In Prob. 4-16, the maximum force transmitted to m is
= /+

To plot this quantity in nondimensional form, multiply by to obtain

^max f^\ f^\ 1 / . \2.i -^max \

which again can be plotted as a function of o)t^ with parameter ft^/nu\y Plot
|io„Zmax/^ol l^max/^o^il ^ function of for equal to 0, 0.20, and 1.0.
4-18 For r > i|, show that the maximum response of the ramp function of Fig. 4.4-2 is equal
to
( iL ‘

which is plotted as Fig. P4-18.

6/r =
2v
Figure P4-18.

4-19 Shown in Fig. P4.5-5 is the response spectrum for the sine pulse. Show that for small
values of ij/r, the peak response occurs in the region t > Determine t^/t^ when
t^/r = f
4-20 An undamped spring-mass system with w = 16.1 lb has a natural period of 0.5 s. It is
subjected to an impulse of 2.0 lb • s, which has a triangular shape with time duration of
0.40 s. Determine the maximum displacement of the mass.
4-21 For a triangular pulse of duration /j, show that when t^/r = the peak response
occurs at t = ij, which can be established from the equation

lirt. ri c\ i 1 ^
277i] fp
2 cos ----- 0.5 - cos 277— ------ 1 - cos------ — =
T 1 t T / ,
found by differentiating the equation for the displacement for t > The response
spectrum for the triangular pulse is shown in Fig. P4-21.