Simplify the following using K-Map 05
(a) Z (A, B,C, D) = (0,2,3,6,7,8,9,10,11,12,13,14,15) (b) F(w. x.y. x) = {3,4,5,7,9,13,14,15)
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Determine the damped natural frequencies and the steady state response of a decoupled damped forced two degrees of freedom system. 10ä1 + 2q1 20q1 10 cos t; 10q2 +4q2 + 40q2 10 cos t

Prove the equivalence between the two statements of the 2nd law of thermodynamics (i.e., a violation of one statement leads to the violatio the other statement)

10 kg of co2 is initially contained at 400 kpa and 300 k. the gas constant for carbon dioxide is 189 j/lkg k) and has a specific heat ratio, k, of 1.289. isentropic expansion then occurs until the pressure is 200 kpa. a) determine the initial volume of co2 in m. b) determine the final temperature in k. c) determine the work done by the system during the expansion kl.