Write the differential equation of motion for the system shown in Fig. and determine the natural frequency of damped oscillation and the critical damping coefficient.​

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)?

An electric kettle is made out of stainless steel, weighs two pounds (when empty) and is equipped with a heating element that consumes 2 kw of electricity. assuming that the water and the kettle are at the same uniform temperature at any moment of time, calculate the shortest possible time to bring 2 quarts of water from room temperature to the onset of boiling

Consider a 1.2 meter high and 2 meter wide glass window whose thickness is 6 mm and thermal conductivity is 0.78 w/m °c. the room temperature is maintained at 24 °c, while the outdoor temperature is -5 °c. the convective heat transfer coefficients on the inner and outer surfaces of the window are 10 w/m2 °c and 25 w/m2 °c respectively. (a) draw the thermal resistance network, etermine the steady rate of heat transfer t e glass window (c) determine the temperature of the inner surface of the window