An earth dam is in danger of failing. A pump is needed to quickly drain the small lake behind the dam. The total energy head required to move water over the top of the dam is 2.43 m. The only pump available is an old 10-cm diameter propeller pump. The power requirement for the motor is 1,000 w and the pump-motor combination has a low efficiency of 50%. Estimate the drawdown (how many centimeters the lake goes down) in the first 2-hour period if the lake has a surface area of 5,000 m2. (Note: Assume that the energy head the pump must overcome does not change much as the lake is lowered in the first 2 hours.)

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?