A spring with an m-kg mass and a damping constant 3 (kg/s) can be held stretched 0.5 meters beyond its natural length by a force of 1.5 newtons. If the spring is stretched 1 meters beyond its natural length and then released with zero velocity, find the mass that would produce critical damping.

Aheat pump using refrigerant-134a heats a house by using underground water at 8°c as the heat source. the house is losing heat at a rate of 60,000 kj/h. the refrigerant enters the compressor at 280 kpa and 0°c, and it leaves at 1 mpa and 60°c. the refrigerant exits the condenser at 30°c. determine: (a) the power input to the heat pump, (b) the rate of heat absorption from the water, and (c) the increase in electric power input if an electric resistance heater is used instead of a heat pump