Determine if the following waveforms are orthogonal over their respective restricted joint intervals, show all work sketch g1 (t) and w (t) in each case. case 1: g1(t)= α1cos(ω1t+ φ1) 0< =t< =1/2f1g2(t)= β2sin(ω2t+ φ2) 0< =t< =1/2f1 α1=constant , φ1= -πβ=constant, φ2= 2πf1=f2= ω1/2πcase 2: g1(t) as in case 1, -1/2f1 < =t< =0g2(t) as in case 1, -1/2f2 < =t< =1/f2all other parameters same as case 1

Heat is added to a piston-cylinder device filled with 2 kg of air to raise its temperature 400 c from an initial temperature of t1 27 cand pressure of pi 1 mpa. the process is isobaric process. find a)-the final pressure p2 b)-the heat transfer to the air.

Ajournal bearing has a journal diameter of 3.250 in with a unilateral tolerance of 20.003 in. the bushing bore has a diameter of 3.256 in and a unilateral tolerance of 0.004 in. the bushing is 2.8 in long and supports a 700-lbf load. the journal speed is 900 rev/min. find the minimum oil film thickness and the maximum film pressure for both sae 20 and sae 20w-30 lubricants, for the tightest assembly if the operating film temperature is 160°f. a computer code is appropriate for solving this problem.

Awall of 0.5m thickness is to be constructed from a material which has average thermal conductivity of 1.4 w/mk. the wall is to be insulated with a material having an average thermal conductivity of 0.35 w/mk so that heat loss per square meter shall not exceed 1450 w. assume inner wall surface temperature of 1200°c and outer surface temperature of the insulation to be 15°c. calculate the thickness of insulation required.