We investigate two stripped-envelope supernovae (SNe) discovered in the nearby galaxy NGC 5806 by the (i)PTF. These SNe, designated PTF12os/SN 2012P and iPTF13bvn, exploded at a similar distance from the host-galaxy center. We classify PTF12os as a Type IIb SN based on our spectral sequence; iPTF13bvn has previously been classified as Type Ib having a likely progenitor with zero age main sequence (ZAMS) mass below ~17 solar masses. Our main objective is to constrain the explosion parameters of iPTF12os and iPTF13bvn, and to put constraints on the SN progenitors. We present comprehensive datasets on the SNe, and introduce a new reference-subtraction pipeline (FPipe) currently in use by the iPTF. We perform a detailed study of the light curves (LCs) and spectral evolution of the SNe. The bolometric LCs are modeled using the hydrodynamical code HYDE. We use nebular models and late-time spectra to constrain the ZAMS mass of the progenitors. We perform image registration of ground-based images of PTF12os to archival HST images of NGC 5806 to identify a potential progenitor candidate. Our nebular spectra of iPTF13bvn indicate a low ZAMS mass of ~12 solar masses for the progenitor. The late-time spectra of PTF12os are consistent with a ZAMS mass of ~15 solar masses. We successfully identify a progenitor candidate to PTF12os using archival HST images. This source is consistent with being a cluster of massive stars. Our hydrodynamical modeling suggests that the progenitor of PTF12os had a compact He core with a mass of 3.25 solar masses, and that 0.063 solar masses of strongly mixed 56Ni was synthesized. Spectral comparisons to the Type IIb SN 2011dh indicate that the progenitor of PTF12os was surrounded by a hydrogen envelope with a mass lower than 0.02 solar masses. We also find tentative evidence that the progenitor of iPTF13bvn could have been surrounded by a small amount of hydrogen.
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