Amachine weighing 19.3 lb is subjected to a harmonic force having a maximum value of 12 lb and a frequency of 300 cycles/min. the clearance for the vibrational movement of the machine is 1 in. design a lightly damped elastic-support system for the machine, so that the machine does not collide in its movement.

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)?