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.

Along steel shaft of 10 cm diameter is austenised at 870°c and then quenched in a liquid at 30oc. the average surface heat transfer coefficient is 2000 w/m2. °c. the relevant thermophysical properties of the shaft are: p=7800 kg/m", k=20 w/mk, cp=0.46 kj/kg.k calculate: a)-the time required for the center temperature to drop to 200°c. b)-the temperature at half-radius at that moment. c)-the amount of heat that had been transferred to the liquid by that time per meter length of the shaft