A mass with mass 4 is attached to a spring with spring constant 25.5625 and a dashpot giving a damping 20. The mass is set in motion with initial position 1 and initial velocity 0. (All values are given in consistent units.) Find the position function x(t):

Acommercial refrigerator with refrigerant-134a as the working fluid is used to keep the refrigerated space at -35°c by rejecting waste heat to cooling water that enters the condenser at 18°c at a rate of 0.25 kg/s and leaves at 26°c. the refrigerant enters the condenser at 1.2 mpa and 50°c. if the compressor consumes 3.3 kw of power, determine (a) the mass flow rate of the refrigerant, (b) the refrigeration load, (c) the cop, and (d) the minimum power input to the compressor for the same refrigeration load.