It is proposed to use liquefied petroleum gas (lpg) in spark-ignition engines. a typical sample of the fuel on a volume basis consists of: 80% propane c3h8, 10% butane c4h10, 10% propene c3h6 the higher heating values of the fuels are 50.38 mj/kg for propane, 49.56 mj/kg for butane, and 48.95 mj/kg for propene. a) show and balance the overall combustion reaction for stoichiometric combustion of 1 mole of lpg with atmospheric air, and determine the stoichiometric f/a and a/f ratios. b) what are the higher and lower heating values per unit mass of lpg?

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?