The Oscillating universe hypothesis (Part ||) : A Balanced Helical Harmonic Oscillator Analogy

This work presents an exploratory conceptual analogy inspired by elementary mechanics, geometry, and cosmology. Rather than proposing a new cosmological theory, the manuscript investigates a simple thought experiment: what if cosmic expansion is viewed through the familiar picture of a balanced helical harmonic oscillator? The framework explores characteristic timescales, harmonic-frequency scales, the hypothetical parameter K_Obaid, and their numerical comparison with established cosmological quantities. The correspondence is presented as a conceptual and dimensional observation, not as evidence that the Universe physically behaves as a harmonic oscillator. The manuscript is a continuation of the author's first DOI-archived conceptual note and is intended to document the development of the analogy in a clearer and more organized form. All assumptions and numerical results are explicitly presented as exploratory and hypothetical, with no claim of a new physical law or replacement of established cosmology.