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Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

Apump is used to circulate hot water in a home heating system. water enters the well-insulated pump operating at steady state at a rate of 0.42 gal/min. the inlet pressure and temperature are 14.7 lbf/in.2, and 180°f, respectively; at the exit the pressure is 60 lbf/in.2 the pump requires 1/15 hp of power input. water can be modeled as an incompressible substance with constant density of 60.58 lb/ft3 and constant specific heat of 1 btu/lb or. neglecting kinetic and potential energy effects, determine the temperature change, in °r, as the water flows through the pump.

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