1. Write the differential equation(s) for the mechanical system shown in Fig. 2.1.(a)-(c) State whether you think the system will eventually decay so that it has no motion at all, given that there are nonzero initial conditions for both masses, and give a reason for your answer

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