Consider the periodic discrete-time exponential time signal x[n] = e^m(2π/N)n

Show that the fundamental period of this signal is N0 = N/ gcd(m, N), where gcd(m, N) is the greatest common divisor of m and N—that is, the largest integer that divides both m and N an integral number of times. For example, gcd(2, 3) = 1, gcd(2, 4) = 2, gcd(8, 12) = 4. Note that N0 = N if m and N have no factors in common

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.

Abrake has a normal braking torque of 2.8 kip in and heat-dissipating cast-iron surfaces whose mass is 40 lbm. suppose a load is brought to rest in 8.0 s from an initial angular speed of 1600 rev/min using the normal braking torque; estimate the temperature rise of the heat dissipating surfaces.

Water at 55c flows across a flat plate whose surface temperature is held constant at 95c. if the temperature gradient at the plate's surface for a given value of x is 18 c/mm, find a) local heat transfer coefficient. b) heat flux