An engineer, tasked with making sure that a skyscraper does not sway during earthquakes or high winds. installs a series of devices to dampen the swaying motion of the building. The devices used can have the amount of damping they prowde adjusted. With the dampers, the engineer determines that the equation of motion of the bridge is: i + 5.256 + 7.1:: = D where s is the amount of displacement due to the sway and o: is setting on the damping devices the engineer has installed. What value ofct (which is a dimensionless number) should the engineer set the devices to so that the sway is clamped as rapidly as possible? Answer: Check 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 driving 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 A 2.5 B 20 Phase Difference (rad) 15 1.0 0.5 00 Driver Frequency (rad/s) O The damping ratio of A is less than that of B and the resonance for both systems has an cross out angular frequency of approximately 2.5 rad/s. O The damping ratio of A is less than that of B but the angular frequency of cross out the resonance for both systems cannot be determined from the plot. O The damping ratio of A is less than that of B but the angular frequency of cross out the resonance for both systems cannot be determined from the plot. O The damping ratio of B is less than that of A and the resonance for both systems has an cross out angular frequency of approximately 2.5 rad/5. O The damping ratio of B is less than that of A but the angular frequency of the resonance cross out for both systems cannot be determined from the plot. O The damping ratio of A is less than that of B and while the resonance for A has an cross out angular frequency of approximately 2.5 rad/s, B does not show a resonance. CheckConsider an underdamped pendulum system 6'\") = Are'37 605(wt). How long does it take for this system to come to rest (if ever)? Give your answer in terms of the parameters of the system A, T. andfer w. IIIIA' B II E :E||o 9s||EI u| % Approximate word count: I) The following equations. all using Sl units unless otherwise noted. describe waves propagating along five different strings, all with the same length and the same tension. Which. if any. of the strings have equal masses? Iftwo or more strings have equal mass, select all of them below. If all the masses are different. select the last option [none of the above]. String A: y(z, t) = (2 cm)sin(31 lt) String B: y(z, t) = (1 cm) sin(lz 43} String C: y(I, t) = (1 cm} sin(3z 4t] String D: y(a:, t) = [1 cm) siJ1(4z 12f) String E: at, '8) = (2 cm) sin(6: 24f) : String A String B String C : String D 2 String E 2 All of the strings have different masses. Check cross out cross out cross out cross out cross out cross out A long. heavy rope hangs straight down from a high balcony on an apartment building. The lower end of the rope hangs about 1.0 m above the ground. If you grab onto the lower end and waggle it back and forth with constant frequency f. a wave travels up the rope. What would happen to the frequency and wavelength of the wave as it travels up the rope? For each property. state whether it would increase, decrease or remain the same, and explain briey (1 2 sentences for each property). llllA' B Il E Ella, ssllg ul 5 Approximate word count: 0