Apositive charge q = 4 nc is placed in the center of a ring of radius r = 5 cm. the ring carries a uniformly distributed negative charge of total magnitude -4 μc. if the charge q moves a small distance from the center x, as indicated in the figure, show that it will describe a simple harmonic motion and calculate the period of the oscillation if the mass of the particle is m = 6 g.

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Two horizontal plates with infinite length and width are separated by a distance h in the z direction. the bottom plate is moving at a velocity u. the incompressible fluid trapped between the plates is moving in the positive x-direction with the bottom plate. align gravity with positive z. assume that the flow is fully-developed and laminar. if the systems operates at steady state and the pressure gradient in x-direction can be ignored, do the following: 1. sketch your system 2. identify the coordinate system to be used. 3. show your coordinates and origin point on the sketch. list all your assumptions. 5. apply the continuity equation to your system. nts of navier stokes equations of choice to your system 7. solve the resulting differential equation to obtain the velocity profile within the system make sure to list your boundary conditions. check units of velocity 8. describe the velocity profile you obtain using engineering terminology. sketch that on the same sketch you provided in (1). 9. obtain the equation that describes the volumetric flow rate in the system. check the units.

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