Consider a cylindrical capacitor that consists of an inner conducting cylinder(a wire) with radiusa, and an outer cylindrical shell of radiusb. the inner cylinder hastotal charge +qand the outer cylindrical shell has total charge−q. a) (2 points) find the surface charge densities on the cylinder and cylindrical shellσaandσb, respectively. b) (2 points) find thee-field everywhere. make a sketch of your solution. c) (2 points) integrate the energy density stored in thee-field. d) (2 points) find the capacitancecof this system, and then use stored energy =12cv2.5.

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.

Apipe with an outside diameter of 15 cm is exposed to an ambient air and surrounding temperature of -20°c. the pipe has an outer surface temperature of 65°c and an emissivity of 0.85. if the rate of heat loss from the pipe surface is 0.95 kw per meter of length, the external convective heat transfer coefficient (h) is: (a) 12.5 w/m"k (b) 18.6 w/mk (c) 23.7 w/mk (d) 27.9 w/mk (e) 33.5 w/mk

Determine the damped natural frequencies and the steady state response of a decoupled damped forced two degrees of freedom system. 10ä1 + 2q1 20q1 10 cos t; 10q2 +4q2 + 40q2 10 cos t