The boeing 747 is an air plane often equipped with four pratt and whitney jt9d engines that can each offer 193.50 kn of thrust. the air plane has a cruise speed of 907 km/hour, and typical cruise altitudes are of 11 km where the air temperature is -56 °c and density is 0.36 kg/m^3. its coefficient of drag at cruise conditions is 0.031, using the total wing area of 511m^2 as the reference area. its maximum take-off mass is 333000 kg a) what is the plane's coefficient of lift during cruise at its maximum take-off mass? b) what percentage of maximum thrust is required to keep the plane cruising? c) what is the plane's maximum angle of ascent? use the coefficient of lift calculated in part a). the following may be of : a cos(x) + bsin(x) = r cos(x-a) where r = va2+52 and a = tan(b/a)

Tom is having a problem with his washing machine. he notices that the machine vibrates violently at a frequency of 1500 rpm due to an unknown rotating unbalance. the machine is mounted on 4 springs each having a stiffness of 10 kn/m. tom wishes to add an undamped vibration absorber attached by a spring under the machine the machine working frequency ranges between 800 rpm to 2000 rpm and its total mass while loaded is assumed to be 80 kg. a) what should be the mass of the absorber added to the machine so that the natural frequency falls outside the working range? b) after a first trial of an absorber using a mass of 35 kg, the amplitude of the oscillation was found to be 10 cm. what is the value of the rotating unbalance? c) using me-3.5 kg.m, find the optimal absorber (by minimizing its mass). what would be the amplitude of the oscillation of the absorber?