Suppose that the trajectory .x.t /; y.t // of a particle
Chapter , Problem 48(choose chapter or problem)
Suppose that the trajectory .x.t /; y.t // of a particle moving in the plane satisfies the initial value problem x00 2y0 C 3x D 0, y00 C 2x0 C 3y D 0; x.0/ D 4; y.0/ D x0 .0/ D y0 .0/ D 0: Solve this problem. You should obtain x.t / D 3 cost C cos 3t; y.t / D 3 sin t sin 3t: Verify that these equations describe the hypocycloid traced by a point P .x; y/ fixed on the circumference of a circle of radius b D 1 that rolls around inside a circle of radius a D 4. If P begins at A.a; 0/ when t D 0, then the parameter t represents the angle AOC shown in Fig. 4.2.8.
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