Generative Artificial Intelligence (GenAI) tools and models have the potential to re-shape educational needs, norms, practices, and policies in all sectors of engineering education. Empirical data, rather than anecdata and assumptions, on how engineering students have adopted GenAI is essential to developing a foundational understanding of students' GenAI-related behaviors and needs during academic training. This data will also help formulate effective responses to GenAI by both academic institutions and industrial employers. We collected two representative survey samples at the Colorado School of Mines, a small engineering-focused R-1 university in the USA, in May 2023 ($n_1=601$) and September 2024 ($n_2=862$) to address research questions related to (RQ1) how GenAI has been adopted by engineering students, including motivational and demographic factors contributing to GenAI use, (RQ2) students' ethical concerns about GenAI, and (RQ3) students' perceived benefits v.s. harms for themselves, science, and society. Analysis revealed a statistically significant rise in GenAI adoption rates from 2023 to 2024. Students predominantly leverage GenAI tools to deepen understanding, enhance work quality, and stay informed about emerging technologies. Although most students assess their own usage of GenAI as ethical and beneficial, they nonetheless expressed significant concerns regarding GenAI and its impacts on society. We collected student estimates of ``P(doom)'' and discovered a bimodal distribution. Thus, we show that the student body at Mines is polarized with respect to future impacts of GenAI on the engineering workforce and society, despite being increasingly willing to explore GenAI over time. We discuss implications of these findings for future research and for integrating GenAI in engineering education.