Express each of the following periodic signals by its Fourier series in all three forms, identify the time period and the harmonics present, compute the signal power and the value, and, for parts (a) and (b), sketch the one-sided and two-sided spectra.

a) x(t) = 4 + 2 sin (4 pi t + pi/4) + 3 sin (16 pi t) + 4 cos (16 pi t)

b) x(t) = sigma_k = -4_k notequalto 0^4 6/k sin (k pi/2) e^-j k pi/3 e^j k 6 pi t

c) x(t) = 2 - 4 cos (8 pi t + 0.25 pi) + 10 sin (12 pi t - pi/3)

Aflywheel accelerates for 5 seconds at 2 rad/s2 from a speed of 20 rpm. determine the total number of revolutions of the flywheel during the period of its acceleration. a.5.65 b.8.43 c. 723 d.6.86

Apipe with an outside diameter of 15 cm is exposed to an ambient air and surrounding temperature of -20°c. the pipe has an outer surface temperature of 65°c and an emissivity of 0.85. if the rate of heat loss from the pipe surface is 0.95 kw per meter of length, the external convective heat transfer coefficient (h) is: (a) 12.5 w/m"k (b) 18.6 w/mk (c) 23.7 w/mk (d) 27.9 w/mk (e) 33.5 w/mk

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.