A weakly damped oscillator with mass m, friction constant b, and spring constant k is being driven near its resonance frequency. (a) Show that the quality factor Q = ωR/2β is approximately ωR/Δω, where β was defined in a class, and Δω is the width of the resonance peak.

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

Different types of steels contain different elements that alter the characteristics of the steel. for each of the following elements, explain what the element does when alloyed with steel.

Determine whether or not it is possible to compress air adiabatically from k to 140 kpa and 400 k. what is the entropy change during this process?