Suppose that two plates of indefinite thickness, initially at different temperatures, are brought into contact at t = 0. plate 1, with thermal properties a1 and k1, is at x < 0 and has initial tempera- ture t1 ; plate 2, with properties a2 and k2 , is at x > 0 and has initial temperature t2 . 1222 determine the temperatures in both plates, expressed as q = (t - t )> (t - t ). is the tem- 212 perature at x = 0 constant or does it vary with time? (hint: it will be to use similarity vari- ables of the form hi = x/[2(ait)^(1/2)].)

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.

How to increase the thermal officiency of an ideal simple rankino cycle? among these methods, which one is the best and why?

In general, how do thermosetting plastics compare to thermoplastics in mechanical and physical properties?