The function f(t) is periodic with period t = 4s. between t=0 and 4s, the function is described by: f(t) =    −1 2 1 0 < t < 1s 1 < t < 3s 3 < t < 4s (a) plot f(t) between t = −8s and t = 8s. (b) determine the exponential fourier coefficients fn of f(t) for n=0, n = ±1s, and n = ±2s. (c) using the result of part (b), determine the compact-form fourier coefficients c0, c1, c2 and c3.

Adouble-strand no. 60 roller chain is used to transmit power between a 13-tooth driving sprocket rotating at 300 rev/min and a 52-tooth driven sprocket. a) what is the allowable horsepower of this drive? b) estimate the center-to-center distance if the chain length is 82 pitches. c) estimate the torque and bending force on the driving shaft by the chain if the actual horsepower transmitted is 30 percent less than the corrected (allowable) power.

The higher the astm grain-size number, the coarser the grain is. a)-true b)-false

Amixture of slurry and mud is to be pumped through a horizontal pipe of diameter 500 mm. the fluid behaves as a bingham plastic with a yield stress of 30 pa and viscosity 0.04 pa.s. describe the effects of the shear stress through a transverse section of the pipe by plotting the variation in shear stress and velocity profile: (i) just before the slurry starts to move (ii) as the slurry flows when the pressure gradient is double that in part (i)