The position of a particle in a fixed inertial frame of reference is given by the vectorwh...

The position of a particle in a fixed inertial frame of reference is given by the vector

where x0, R, and Ω. are constants.

(a) Show that the particle moves in a circle with constant speed.

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(b) Find two coupled, first-order differential equations of motion drat relate the components of position, x′ and y′, and the components of velocity,  and  of the particle relative to a frame of reference rotating with an angular velocity ω =kω.

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(c) Letting the fixed and rotating frames of reference coincide at times t = 0 and letting u′= x′ + iy′, find u′(t), assuming drat Ω ≠ −ω). (Note: )