(Properties of Continuous Systems) Determine (with justification) whether the follow- ing 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(t) denotes the system output and z(t) is the system input. a) y(t) = (t - 2)2(t+2)
b) y(t) = 2(t-1) + x(4- t)
c) y(t) = x(sin(t))
d) (Optional, not graded) y(t) = { 0, So r(t – T)dt, z(t) <1, r(t) > 1.

The temperature of air decreases as it is compressed by an adiabatic compressor. a)- true b)- false

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.