17. Periodic Motion
Simple Harmonic Motion of Pendulums
17. Periodic Motion Simple Harmonic Motion of Pendulums
30PRACTICE PROBLEM
Gravitational force can be used as a restoring force for a mass mo oscillating in a hollow drilled through a spherical mass's center (a diameter). For a sphere of mass Ms, and radius Rs, it is proven that an oscillating mass with position x where r ≤ x ≤ R experiences a net gravitational force from the spherical mass enclosed by r where r ≤ x, while the mass of spherical shell at x > r does not contribute to the net gravitational force of the oscillating mass. For a sphere with even density, derive an expression for the gravitational force on the oscillating mass. Express the result using Ms, Rs, x, mo, and any desired constant(s).
Gravitational force can be used as a restoring force for a mass mo oscillating in a hollow drilled through a spherical mass's center (a diameter). For a sphere of mass Ms, and radius Rs, it is proven that an oscillating mass with position x where r ≤ x ≤ R experiences a net gravitational force from the spherical mass enclosed by r where r ≤ x, while the mass of spherical shell at x > r does not contribute to the net gravitational force of the oscillating mass. For a sphere with even density, derive an expression for the gravitational force on the oscillating mass. Express the result using Ms, Rs, x, mo, and any desired constant(s).