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Expanding & Contracting Sphere Harmonic Motion Model

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I am trying to model the harmonic motion of an expanding and contracting sphere. In this case, the origin of the spherical oscillation is not a point source but rather a sphere with a time varying radius. i.e the volume of the sphere is expanding and contracting to a non point source.

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Solution Summary

A sphere contraction and expansion motion as a harmonic motion is modelled here, and it's time period is estimated.

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Assume sphere non-deformed radius is R, corresponding volume V and surface area A

V = (4 pi/3)R^3
A = 4 pi R^2

Let us assume at time t, there is a small deformation, and sphere radius is deformed by delta_r.
Correspondingly, change in volume = delta_V = 4 pi R^2 delta_r [ delta_V ...

Solution provided by:
Amrit Lal Ahuja, PhD (IP)
Education
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
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