The study of baryon resonances provides a deeper understanding of the strong interaction because the dynamics and relevant degrees of freedom hidden within them are reflected by the properties of the excited states of baryons. Higher-lying excited states at and above 1.7 GeV/c² are generally predicted to have strong couplings to final states involving a heavier meson, e. g. one of the vector mesons, ρ, ω, φ, as compared to a lighter pseudoscalar meson, e.g. π and η. Decays to the ππN final states via π∆ also become more important through the population of intermediate resonances. We observe that nature invests in mass rather than momentum. The excited states of the nucleon are usually found as broadly overlapping resonances which may decay into a multitude of final states involving mesons and baryons. Polarization observables make it possible to isolate single-resonance contributions from other interference terms. The CLAS g9 (FROST) experiment, as part of the N∗ spectroscopy program at Jefferson Laboratory, accumulated photoproduction data using circularly- and linearly-polarized photons incident on a transversely-polarized butanol target (g9b experiment) in the photon energy range 0.3 − 2.4 GeV & 0.7 − 2.1 GeV, respectively. In this work, the analysis of reactions and polarization observables which involve two charged pions, either in the fully exclusive reaction γp → pπ⁺π⁻ or in the semi-exclusive reaction with a missing neutral pion, γp → pπ⁺π⁻ (π⁰) will be presented. For the reaction γp → pπ⁺π⁻ , eight polarization observables (I[superscript s], I[superscript c], P[subscript x], P[subscript y], P[superscript s][subscript x,y], P[superscript c][subscript x,y]) have been extracted. The high statistics data rendered it possible to extract these observables in three dimensions. All of them are first-time measurements. The fairly good agreement of I[superscript s] and I[superscript c] obtained from this analysis with the experimental results from a previous CLAS experiment provides support for the first time measurements. For the reaction γp → pω → pπ⁺ π⁻ (π⁰), five polarization observables (T , Σ, F , H, P ) have been extracted, four of which are first-time measurements at all energies. This analysis thus represents a comprehensive program on vector-meson photoproduction: The ω is observed and studied directly from the data and the polarization observables for the (broad) ρ can be extracted from the double-pion reaction in a partial-wave analysis. The 13 polarization observables extracted in this analysis substantially augment the world database of polarization observables for these reactions and are expected to play a crucial role in identifying the contributing baryon resonances.