Consider a differerential equation: x^m+2kx+x=0;x 00 + 2kx0 + x = 0; x(0) = 0, x0 (0) = b where primes denote differentiation with respect to time, t. Find the solution of the differential equation for the cases (i) k2 > 1, (ii) k2 < 1 and (iii) k2 = 1.​

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.

Avolume of 2.65 m3 of air in a rigid, insulated container fitted with a paddle wheel is initially at 264 k, 5.6 bar. the air receives 432 kj by work from the paddle wheel. assuming the ideal gas model with cv = 0.71 kj/kg • k, determine for the air the amount of entropy produced, in kj/k

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