TABLE OF CONTENTS We've just seen that vibrations can be avoided in a forced mass by the addition of a vibration absorber. However you might be a bit doubtful. After all, the second mass could counter the externally applied force only because it was oscillating exactly out of phase with this force. The obvious question is then, What if the force is not exactly out of phase with the second mass? In this case, we'll have an unbalanced force on the first mass, and it should move. How does the real world get around this problem?
Figure 4.17 shows the actual response (found from numerically integrating the equation of motion) of both the first and second masses of a vibration absorber problem for a system shown earlier (Figure 4.11b). Note that the primary mass does not remain stationary. However, it's important to realize that the vibrations are bounded. If the force and the second mass weren't correctly phasealigned, we'd have a resonance condition and the oscillations would grow. Since we certainly don't have growing oscillations, the force and the second mass are correctly phase-aligned. The vibrations occur because with no damping in the system, the homogeneous solution (that due to initial conditions) never dies out; it "rings" forever. This is the vibration we're seeing that due to initial conditions. To avoid this solution, we can carefully choose our initial conditions to obtain the vibration absorption we want. If the initial conditions are chosen so...
