(a) what is the period of the forced oscillation? what is the numerical value (modulo 2π) of the angle α defined by (4)?

(b) in this question you are asked to modify the file lab06ex1.m in order to plot the complementary solution of (1), that is, the first term in (2). first define in the file the angle α (alpha) using (4), then evaluate the complementary solution yc by subtracting the quantity c cos(ωt − α) from the numerical solution y. plot the resulting quantity. does it look like an exponentially decreasing oscillation? why or why not? include the modified m-file and the corresponding plot.

An external consultant recommends that a plant installs a bank of capacitors for power factor correction. this will reduce the peak electrical demand charges by an average of 93 kw every month. the plant current pays $13 per kw in peak demand charges. the capacitor bank will include 223 kw of fixed capacitors, and 183 of variable capacitors. the fixed capacitors cost $59 per kw, and the variable capacitors will cost $65 per kw. the consultant charges 21% of the equipment costs to install the capacitors. because this project will reduce the demand for the electric utility, they are prepared to provide a one-time rebate of $42 per kw of reduced demand. what is the simple payback period for this project (in years)?