Thirty pieces of structural timber of the same dimensions were subjected to an increasing lateral force until they broke. The measured force in pounds required to break them is given in the following list. Use MATLAB to plot the relative frequency histogram. Compute the mean and standard deviation of the data and use them to estimate the lower and upper limits of strength corresponding to 68% and 96% of timber pieces. 243
404
497
132
457
236
464
500
196
347
389
605
535
217
628
137
577
660
143
123
441
569
417
372
231
865
205
439
675
725

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)?

Amass-spring-viscous damper system of mass 3 kg has a frequency of 100 rad/s and is critically damped. its initial conditions are x(0)-3 mm and (0)-2.3 m/s. does the system overshoot its equilibrium position? prove your answer

Around steel bar, made from material with a yield stress of 750mpa, is loaded so that it has stresses co locations of maximum normal stress and maximum shear stress. use maximum shear stress and maximum distortion energy theories to calculate the safety factors for initial yielding failures.