Find the fourier transform f. t. for the following signals using the linearity property. g(t) = a rect(t/t)+e^-2t u(t)

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?

An electric kettle is made out of stainless steel, weighs two pounds (when empty) and is equipped with a heating element that consumes 2 kw of electricity. assuming that the water and the kettle are at the same uniform temperature at any moment of time, calculate the shortest possible time to bring 2 quarts of water from room temperature to the onset of boiling

Determine the time of the day and month of the year at which the peak sensible cooling load occurs for a top floor, north-eastern corner room of an office building in durban for the following conditions: floor area: 8 x 8 x 3 m east and north walls: 115 mm face brick (outside), 20 mm air space, 115 mm ordinary brick (inside) with 15 mm plaster roof construction: suspended plasterboard ceiling, 450 mm air space, 150 mm concrete, 75mm screed, waterproofing no heat transfer across other surfaces window area 3x 1,5 m high in north wall only. ordinary glass with venetian blinds. lights and occupants : from 07: 00 to 18: 00 average light density: 25 w/m2 number of occupants : 5 seated, light office work room temperature 24°c