The temperature distribution across a wall 0.3 m thick at a certain instant of time is T(x) = a + bx + cx2, where T is in degrees Celsius and x is in meters, a = 190 oC, b = -205 oC/m, and c = 20 oC/m2. The wall has a thermal conductivity of 1 W/mK .

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.

Water at 55c flows across a flat plate whose surface temperature is held constant at 95c. if the temperature gradient at the plate's surface for a given value of x is 18 c/mm, find a) local heat transfer coefficient. b) heat flux

Calculate the bore of a cylinder that has a stroke of 18 inches and an extension time of 6 seconds at a flow rate of 4 gal/min.