Suppose you have a string of n christmas lights, numbered 1, . . , n that are wired in series. one of the lights is broken and you want to find out which. you have a multimeter that you can use to test whether any section of the string works. i. e., test(i, j) returns true if lights i through j (inclusive) are all working, and false if one of them is broken. design a recursive algorithm to identify the broken light (you should assume there is exactly one) and analyze its runtime.

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.

Water in a partially filled large tank is to be supplied to the roof top, which is 8 m above the water level in the tank, through a 2.2-cm-internal-diameter pipe by maintaining a constant air pressure of 300 kpa (gage) in the tank. if the head loss in the piping is 2 m of water, determine the discharge rate of the supply of water to the roof top in liters per second.

The sum of the normal stresses does not change as the stress state rotates through an angle. a)-trune b)- false