An object of mass m slides on a horizontal platform. the platform rotates at a counterclockwise rate w around a vertical axis. the object suffers linear drag f = -2mγū, where v is the velocity relative to the platform, with γ > 0. this is the system discussed in the lecture notes, with the addition of a true force: linear drag. a) find the coupled linear differential equations governing x(t) and y(t). define the complex dynamical coordinate ψ(t) = x(t) + iy(t), and derive a single complex linear differential equation that governs . you should get ψ =w2 ψ-2γ ψ - 2iwψ seek solutions in the form = 1.est and solve for the two roots s.

An charge with mass m and charge q is emitted from the origin, (x, y)=(0,0). a large, flat screen is located at x=l. there is a target on the screen at y position y(h), where y(h) > 0. in this problem, you will examine two different ways that the charge might hit the target. ignore gravity in this problem. 1.assume that the charge is emitted with velocity v(0) in the positive x direction. between the origin and the screen, the charge travels through a constant electric field pointing in the positive y direction. what should the magnitude e of the electric field be if the charge is to hit the target on the screen? express your answer in terms of m, q, y(h), v(0), and l. 2.now assume that the charge is emitted with velocity v(0) in the positive y direction. between the origin and the screen, the charge travels through a constant electric field pointing in the positive x direction. what should the magnitude e of the electric field be if the charge is to hit the target on the screen? express your answer in terms of m, q, y(h), v(0), and l.