Your business reclaims metal waste for reprocessing. You know of a company (ABC) that just installed a new machining process line that produces 1000 MT/yr of a waste powder that is 97% aluminum and 0.05% platinum (the remainder is other impurities). You can invest in a process to reclaim pure platinum and pure aluminum from that powder, but it costs $30 MM to build and $3 MM/yr to operate. You are required to have a simple payback of at most three years for any capital investment. If ABC gives you the waste free of charge, should you proceed to construct the reclamation system? If you build the new reclaiming system, what is the maximum price you can pay ABC per pound of waste powder but still meet the investment criteria?

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?