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A particle of mass m moves in the plane R2 under the influence of an elastic band tying it to the origin. The length of the band is negligible. Hooke's law states that the force on the particle is always directed toward the origin and is proportional to the distance from the origin. Write the force field and verify that it is conservative and central. Write the equation F = ma for this case and solve it. (Compare Section 1.) Verify that for "most" initial conditions the particle moves in an ellipse.

A particle of mass m moves in the plane R2 under the influence of an elastic band tying it to the origin. The length of the band is negligible. Hooke's law states that the force on the particle is always directed toward the origin and is proportional to the distance from the origin. Write the force field and verify that it is conservative and central. Write the equation F = ma for this case and solve it. (Compare Section 1.) Verify that for "most" initial conditions the particle moves in an ellipse.

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A particle of mass m moves in the plane R² under the influence of an elastic band tying it to the origin. The length of the band is negligible. Hooke's law states that the force on the particle is always directed toward the origin and is proportional to the distance from the origin. Write the force field and verify that it is conservative and central. Write the equation F = ma for this case and solve it. (Compare Section 1.) Verify that for "most" initial conditions the particle moves in an ellipse. - Kx: V(x) F(x) dx² dt² m K || x || ² 2 > x ER² - grad V -Kx "Most" initial conditions means the set of (x, v) E R² X R2 such that v is not collinear with x.
Transcribed Image Text:A particle of mass m moves in the plane R² under the influence of an elastic band tying it to the origin. The length of the band is negligible. Hooke's law states that the force on the particle is always directed toward the origin and is proportional to the distance from the origin. Write the force field and verify that it is conservative and central. Write the equation F = ma for this case and solve it. (Compare Section 1.) Verify that for "most" initial conditions the particle moves in an ellipse. - Kx: V(x) F(x) dx² dt² m K || x || ² 2 > x ER² - grad V -Kx "Most" initial conditions means the set of (x, v) E R² X R2 such that v is not collinear with x.
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