(Properties of Discrete Systems) Determine (with justification) whether the following systems are (i) memoryless, (ii) causal, (iii) invertible, (iv) stable, and (v) time invariant. For invertibility, either find an inverse system or an example of two inputs that lead to the same output. Note that y[n] denotes the system output and r[n] denotes the system input. a) y[n] = x[n]2[n – 1] x[n + 1] Sz{n-1), n<0, b) y[n] = 1 «[n +1], n>0. c) y[n] = cos(x[n])

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.

Determine whether or not it is possible to compress air adiabatically from k to 140 kpa and 400 k. what is the entropy change during this process?

Shafts are machine elements that are used to a) carry axial loads b) direct shear loads c) transmit power d) rotate at constant speed e) none of the above circular and square shafts subjected to the same torque under the same circum behave a) the same way b) almost the same way