Mathieu's equation, defined as, đều gt2 + [w2 + 2e cos(2t)] u = 0, describes the stability of a pendulum with natural frequency w whose pivot point is oscillated in the vertical direction at a frequency of 2 and amplitude of 2€. a) assume a regular perturbation expansion, u= u(t) + eui(t) + and solve for uo, uz if the initial conditions are u(0) = 1 and du (0) = 0. b) what modes are resonant at order ? c) write down the equation for order o(42) and determine what frequencies are resonant at the next order.

Which type of circuit is becoming more common in residential electrical design and construction? a. hazardous-area circuit b. three-phase circuit c. 480-volt circuit d. communication circuit

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)

The charge on a charged sphere is: a)concentrated at its centerb)distributed uniformly throughout its volumec)clustered on its centerd)distributed uniformly over its surface