I am starting University in September, 2014. I have some knowledge already on classical mechanics as I took optional Applied Math courses (called Mechanics 1 and Mechanics 2) in my mathematics A-Level. I am also self-studying the book Classical Mechanics by Goldstein, Poole and Safko to gain a deeper understanding of the subject.
Pretty much all of the universities I am applying spend freshman year teaching Calculus, Classical Mechanics, Introuctory Chemistry, Thermodynamics and Introductory Biology. There are courses on Modern Physics, Introductory Quantum Mechanics and Special Relativity in the second semester but most of the real stuff starts in the second year if you select something like Physics or (Applied or otherwise) Mathematics as a major.
Now, the thing is, I like doing experiments and formulating equations. I was just wondering if I could, perhaps, write a research paper that formulates some simple effective theory, or perhaps deals with the applications of previous classical mechanical theories in new conditions, or details new experimental ways to test those theories (excuse my vagueness, university is about nine months away and I've only started learning about this stuff) and have that research paper printed in a half-decent journal. Even if it isn't printed in a journal and I have to publish it myself via my university or otherwise, will it be important enough to be mentioned in the applications for MS and PhD. programmes of high-ranked universities like Cambridge, MIT and ETH Zurich after I complete my BS?