Your goal is to navigate a robot out of a maze. The robot starts in the center of the maze facing north. You can turn the robot to face north, east, south, or west. You can direct the robot to move forward a certain distance, although it will stop before hitting a wall.

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.

Afull journal bearing has a journal diameter of 27 mm, with a unilateral tolerance of -0.028 mm. the bushing bore has a diameter of 27.028 mm and a unilateral tolerance of 0.04 mm. the l/d ratio is 0.5. the load is 1.3 kn and the journal runs at 1200 rev/min. if the average viscosity is 50 mpa-s, find the minimum film thickness, the power loss, and the side flow for the minimum clearance assembly.

Air enters a horizontal, constant-diameter heating duct operating at steady state at 290 k, 1 bar, with a volumetric flow rate of 0.25 m°/s, and exits at 325 k, 0.95 bar. the flow area is 0.04 m2. assuming the ideal gas model with k = 1.4 for the air, determine (a) the velocity at the inlet and exit, each in m/s, and (c) the rate of heat transfer, in kw flow rate, in kg/s, (b) the mass kg 0.3