Consider the periodic signal x(t) = cos(pi t)-2-sin(2 pi t). let y(t) be the first derivative fo x(t). determine the fundamental period of y(t) and the value of the coefficients of the fourier series of y(t) indicate how much power is carried by the first harmonic component, i. e., p1, and how much power is carried by the second harmonic component, i. e., p2 of signal y(t)

Aheat pump with refrigerant-134a as the working fluid is used to keep a space at 25°c by absorbing heat from geothermal water that enters the evaporator at 500c at a rate of 0.065 kg/s and leaves at 40°c. the refrigerant enters the evaporator at 20°c with a quality of 23 percent and leaves at the inlet pressure as saturated vapor. the refrigerant loses 300 w of heat to the surroundings as it flows through the compressor and the refrigerant leaves the compressor at 1.4 mpa at the same entropy as the inlet. determine: (a) the degrees of subcooling of the refrigerant in the condenser, b)-the mass flow rate of the refrigerant . (c) the heating load and the cop of the pump, and d)-the theoretical minimum power input to the compressor for the same heating load.