3. find the fourier series coecients x[k] of the periodic signal x(t) with time period 6 given below x(t) = ( 1; 4 t 8 0; 8 < t 10 write your answer in terms of a sinc function, i. e., as x[k] = a sinc(bk). what are a and b? a may be complex. find the values of k for which x[k] is zero. based on this, can you say which frequencies (in rad/s) are present in the signal ?

Apump is used to circulate hot water in a home heating system. water enters the well-insulated pump operating at steady state at a rate of 0.42 gal/min. the inlet pressure and temperature are 14.7 lbf/in.2, and 180°f, respectively; at the exit the pressure is 60 lbf/in.2 the pump requires 1/15 hp of power input. water can be modeled as an incompressible substance with constant density of 60.58 lb/ft3 and constant specific heat of 1 btu/lb or. neglecting kinetic and potential energy effects, determine the temperature change, in °r, as the water flows through the pump.

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Air is compressed isentropically from an initial state of 300 k and 101 kpa to a final temperature of 1000 k. determine the final pressure using the following approaches: (a) approximate analysis (using properties at the average temperature) (b) exact analysis