The company you work for signed a contract with a security firm to control access to company grounds and corporate offices. The contract amount was for $140,000 for the first year, renewable each year for up to a total of 5 years at the same cost plus a percentage increase equal to the inflation rate for the preceding year. Your boss asked you to calculate the expected cost in the final year of the contract (year 5), assuming the inflation rate is 3% for the next 3 years and 5% for the last one.

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?