Assume your hometown is growing so rapidly that another water tower isnecessary to meet the needs of the community. The engineers predict that the water tower will need to hold 1.00 x 10^6 kilograms of water with a density of 999 kilograms per cubic meter. The tower is to be a perfect cylinder with a flat top. They engineers require that the structure be 50 feet in height. What must be the diameter of the tower to accomodate the required volume?

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?