1. Solve the boundary value problem y'' + 2y' + y = 0 with boundary conditions y(0) = 0 and y(1) = 1 using the finite difference method. Write a matlab code that will take as input the number of segments n and will output y(x). Plot the solution for 4, 10, 14 and 20 segments.

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.

Arigid tank contains 10 kg of air at 137 kpa (abs) and 21°c. more air is added to the tank until the pressure and temperature rise to 242 kpa (abs) and 32°c, respectively. determine the amount of air added to the tank. [r-0.287 kj/kg k]

Brief discuss how the presence of dislocations in crystal structures can be an advantage and a disadvantage to engineer and designers.