Question 13.3.1: Design of a Vibration Absorber A certain machine with suppor...

The frequency of the applied force is ω = 2π(4) = 8π rad/sec. The absorber’s design requires that ω_{n_{2}} = ω = 8π . Thus
ω_{n_{2}} = \sqrt{\frac{k_{2}}{m_{2}}} = 8 π
Solve for the mass:
m_{2} = \frac{k_{2}}{64 π^{2}}
The maximum allowable clearance is 0.5 in. = 1/24 ft. Using (13.3.12), we obtain

X_{2} = |X_{2}(jω)| = \frac{1}{k_{2}} F              (13.3.12)
\frac{1}{24} = \frac{F}{k_{2}} = \frac{2}{k_{2}}
or k_{2} = 48  lb/ft. Thus, the absorber’s mass must be
m_{2} = \frac{k_{2}}{64 π^{2}} = \frac{48}{64 π^{2}} = 0.076  slug