3/118 The light rod is pivoted at O and carries the 5‐ and 10‐lb particles. If the rod is released from rest at θ = 60° and swings in the vertical plane, calculate (a) the velocity v of the 5‐lb particle just before it hits the spring in the dashed position and (b) the maximum compression x of the spring. Assume that x is small so that the position of the rod when the spring is compressed is essentially horizontal.

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)?