Discrete-time signals with different frequencies can be equal; this is one manifestation of aliasing and folded aliases. Determine which of the following discrete-time cosine signals are equal (i. e., plots of xi[n]versus n will be identical):

x_1[n] = cos (0.9pi n + 0.1pi)
x_2[n] = cos (-2.9pi n + 0.1pi)
x_3[n] = cos (5.1pi n - 0.1pi)
x_4[n] = cos (6.9pi n - 0.1pi)
x_5[n] = cos (-7.1pi n - 0.1pi)

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.

Burgers vector is generally parallel to the dislocation line. a)-true b)-false

An ideal otto cycle with air as the working fluid has a compression ratio of 8. the minimum and maximum temperatures in the cycle are 300 k and 1340 k. use constant specific heats at room temperature to determine (a) the amount of heat transferred to the air during the heat- addition kj/kg, (b) the thermal efficiency, and (c) the thermal efficiency of a carnot cycle ope limits. process, in rating between the same temperature