{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"frontierscience","formal_name":"FrontierScience","introduction":"専門的な科学課題を解く能力を評価するベンチマークです。公開データはolympiadとresearchに分かれ、競技問題と研究課題を区別して扱います。\n\nFrontierScience evaluates the ability to solve expert-level scientific tasks. Its public data separates olympiad and research problems so that competition and research tasks can be examined independently.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/openai/frontierscience","indexing_mode":"noindex"},"task_id":"606fdb69-d7a0-55df-a02b-98e07ab8d607","task_key":"olympiad--test--70929247~2da356~2d4a12~2d8534~2d49fd885f0c3e","task_revision_id":"1","upstream_id":"70929247-a356-4a12-8534-49fd885f0c3e","short_description":"Consider a pendulum with a length `\\( l \\)` and a mass `\\( m \\)` at the end,…","config":"olympiad","split":"test","body":"{\"problem\":\"Consider a pendulum with a length `\\\\( l \\\\)` and a mass `\\\\( m \\\\)` at the end, where the mass of the rod is negligible and the pendulum bob is treated as a point mass. The pendulum is placed inverted, with the bob at the top, and the lower end of the rod oscillates vertically with `\\\\( y(t)=a\\\\cos\\\\Omega t \\\\)`. Assume `\\\\( a≪l \\\\)` and ` \\\\( \\\\Omega \\\\gg \\\\sqrt{g/l} \\\\)`, where `\\\\( g \\\\)` is the gravitational acceleration. Determine the condition for stable equilibrium of the angle between the rod and the vertical at `\\\\( θ=0 \\\\)`. Your answer must in the form of an inequality for \\\\\\\\( \\\\\\\\Omega \\\\\\\\) in terms of \\\\\\\\( g \\\\\\\\), \\\\\\\\( l \\\\\\\\), and \\\\\\\\( a \\\\\\\\).\\n\\nThink step by step and solve the problem below. At the end of your response, write your final answer on a new line starting with “FINAL ANSWER”. It should be an answer to the question such as providing a number, mathematical expression, formula, or entity name, without any extra commentary or providing multiple answer attempts.\",\"subject\":\"physics\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/openai/frontierscience","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}