圆锥摆

分析

• 绳子的张力T，方向沿细绳向上。
• 竖直方向的重力mg

${\displaystyle T\sin \theta ={\frac {mv^{2}}{r}}\,}$

${\displaystyle T\cos \theta =mg\,}$

${\displaystyle {\frac {g}{\cos \theta }}={\frac {v^{2}}{r\sin \theta }}}$

${\displaystyle v={\frac {2\pi r}{t}}}$

v替换到原先式子中，得到：

${\displaystyle {\frac {g}{\cos \theta }}={\frac {({\frac {2\pi r}{t}})^{2}}{r\sin \theta }}={\frac {(2\pi )^{2}r}{t^{2}\sin \theta }}}$

${\displaystyle g={\frac {4\pi ^{2}r\cos \theta }{t^{2}\sin \theta }}}$

${\displaystyle \sin \theta ={\frac {r}{L}}}$

${\displaystyle t=2\pi {\sqrt {\frac {L\cos \theta }{g}}}}$

参考文献

1. ^ O'Connor, J.J.; E.F. Robertson. Robert Hooke. Biographies, MacTutor History of Mathematics Archive. School of Mathematics and Statistics, Univ. of St. Andrews, Scotland. August 2002 [2009-02-21]. （原始内容存档于2009-03-03）.
2. ^ Nauenberg, Michael. Robert Hooke's seminal contribution to orbital dynamics. Robert Hooke: Tercentennial Studies. Ashgate Publishing: 17–19. 2006. ISBN 0-7546-5365-X.
3. ^ Beckett, Edmund (Lord Grimsthorpe). A Rudimentary Treatise on Clocks and Watches and Bells, 6th Ed.. London: Lockwood & Co. 1874: 22–26 [2015-11-25]. （原始内容存档于2016-04-29）.
4. Clock. Encyclopaedia Britannica, 9th Ed. 6. Henry G. Allen Co.: 15. 1890 [2008-02-25].