An accelerometer is used to measure the amplitude of a simple sinusoidal oscillation with period of 0.027 seconds. if the output voltage from the accelerometer is 0.35 vpp , and the accelerometer calibration is 0.138 v/g, what is the displacement sensed by the accelerometer in mm? (hint: formulate an expression for sinusoidal motion like x(t) = x0 sin(ωt) and then recall how acceleration and displacement are related to find a similar expression for the measured acceleration.)

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)?