Two identical mass-spring systems, A and B, with different damping ratios are driven by an external force with a variable frequency. The phase difference between the drive force and the displacement of the system is plotted as a function of the drive angular frequency and is shown below for both A and B. Which of the statements below is correct? 3.0 Phase Difference (rad) 1 0.5 A B 0.0 4 Q 0 Driver Frequency (rad/s) Show Transcribed Text D Select one: The damping ratio of A is less than that of B and the resonance for both systems has an angular frequency of approximately 2.5 rad/s. The damping ratio of A is less than that of B but the angular frequency of the resonance for both systems cannot be determined from the plot. The damping ratio of B is less than that of A and the resonance for both systems has an angular frequency of approximately 2.5 rad/s. The damping ratio of B is less than that of A but the angular frequency of the resonance for both systems cannot be determined from the plot. The damping ratio of A is less than that of B and while the resonance for A has an angular frequency of approximately 2.5 rad/s, B does not show a resonance.

Some people modify cars to be much closer to the ground than when manufactured. Should they install stiffer springs? Explain your answer.

Consider the damped oscillator illustrated in Figure 12.16a. The mass of the object is 375 g, the spring constant is 100 N/m, and b = 0.100 N s/m. (a) Over what time interval does the amplitude drop to half its initial value? (b) What If? Over what time interval does the mechanical energy drop to half its initial value? (c) Show that, in general, the fractional rate at which the amplitude decreases in a damped harmonic oscillator is one-half the fractional rate at which the mechanical energy decreases.

How would a car bounce after a bump under each of these conditions? (a) overdamping (b) underdamping (c) critical damping