Use the general algorithm to transform the following pushdown automaton into a context-free grammar. this automaton has 4 states: the starting state s, the reading state r, the checking state c, and the final state f. the transitions are as follows: from s to r, the transition is: ε, ε → $; from r to r, the transitions are: a, ε → a; b, ε → b; from r to c, we have a jump ε, ε → ε. from c to c, the transitions are: a, a → ε b, b → ε from c to f, the only transition is: ε, $ → ε. show, step-by-step, how the resulting grammar will generate the sequence abba.

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.

The higher the astm grain-size number, the coarser the grain is. a)-true b)-false

Atmospheric air has a temperature (dry bulb) of 80° f and a wet bulb temperature of 60° f when the barometric pressure is 14.696 psia. determine the specific humidity, grains/lb dry air. a. 11.4 c. 55.8 d. 22.5 b. 44.1