two capacitors , one charged and the other uncharged are connected in parallel. Prove that when equilibrium is reached, each capacitor carries a fraction of the initial charge equal to the ratio of its capacitance of the two sum of capacitances . Show that the final energy is equal to initial energy, and derive a formula in terms of charge and capacitances of the two capacitor

Thermal stresses are developed in a metal when its a) initial temperature is changed b) final temperature is changed c) density is changed d) thermal deformation is prevented e) expansion is prevented f) contraction is prevented

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

Asimple speed reducer is composed of 2 spur gears. the pinion gear has a pitch diameter of 0.75" and 36 teeth while the driven gear has a pitch diameter of 4.0" and 192 teeth. a)-what is the diametral pitch of each gear? b)-if an electric motor rotating ccw at 3000 rpm is coupled to the pinion, what is the rotational speed of the driven gear? c)-if the torque delivered to the pinion is 1 n-m, what is the torque on the driven gear? d)-what is the power transmitted by the gear train?