Wave Pendulum and Prime Numbers: A Spectral Isomorphism via Riemann Zeta Zeros

This paper explores a spectral isomorphism between wave pendulum dynamics and prime number patterns via Riemann zeta zeros. We demonstrate that both systems share mathematical structures based on superposition of discrete frequency components, leading to comparable interference phenomena. The temporal evolution of the wave pendulum relates to logarithmic scaling in prime distributions, with both patterns emerging from similar spectral principles mediated by Riemann zero contributions. Analytical derivation and numerical analysis support this correspondence, suggesting connections between mechanical systems and number-theoretical concepts through spectral geometry.