- 1、本文档共10页,可阅读全部内容。
- 2、原创力文档(book118)网站文档一经付费(服务费),不意味着购买了该文档的版权,仅供个人/单位学习、研究之用,不得用于商业用途,未经授权,严禁复制、发行、汇编、翻译或者网络传播等,侵权必究。
- 3、本站所有内容均由合作方或网友上传,本站不对文档的完整性、权威性及其观点立场正确性做任何保证或承诺!文档内容仅供研究参考,付费前请自行鉴别。如您付费,意味着您自己接受本站规则且自行承担风险,本站不退款、不进行额外附加服务;查看《如何避免下载的几个坑》。如果您已付费下载过本站文档,您可以点击 这里二次下载。
- 4、如文档侵犯商业秘密、侵犯著作权、侵犯人身权等,请点击“版权申诉”(推荐),也可以打举报电话:400-050-0827(电话支持时间:9:00-18:30)。
查看更多
Notes on mechanical vibrations NYU Courant(在机械振动纽约大学报》)
Notes on mechanical vibrations
Stephen Childress
April 13, 2005
1 Masses and springs- the linear oscillator
These notes will be related to sections 1-29 of the text. I will indicate between
brackets [..] references to the sections closest to the discussion here.
We are will study mechanical vibrations for two reasons: on the math side, it
will introduce second-order ODEs (involving two differentiations) in the context
of Newton’s equations of motion. We will revisit the idea of a phase plane in
two variables, as we have used it in the study of two-species population models,
but now with a physical meaning derived from Newtonian physics.
The centerpiece of Newtonian physics is the second law [1-3,5] , stating that
a body of mass m will accelerate when a force F is applied to it, in such a way
that
2
d x
m dt2 = F. (1)
Here x(t) is the position of the mass- for simplicity think of a uniform sphere
with x denoting the position of its center. (In general x will denote the center
of mass of the body.). A better way to state this law is in terms of momentum.
The momentum of the mass is mv where v = dx is the velocity of the body (of
dt
it’s center of mass). Then Newton’s second law becomes
dmv
= F, (2)
dt
i.e. it states that the rate of change of the momentum of the body is equal to
the instantaneous force applied to the body.
In addition to a mass, we also want to introduce a spring with sp
您可能关注的文档
- N ESENTATIO lifttrade.it(N ESENTATIO lifttrade.it).pdf
- Nanomaterials for Advanced Applications (纳米材料为先进的应用程序).pdf
- N R C H R VISION E S Great Maths Teaching (N R C H R愿景E S 伟大的数学教学).pdf
- NAFTA Powertrain Outlook IHS(北美自由贸易协定动力系统前景 IHS).pdf
- NanoStar NanoFree 300 m Solder Bump (NanoStar NanoFree 300焊接凸点).pdf
- NAPA now Carries Aisin Water Pump Timing Belt (纳帕现在Aisin水泵正时皮带).pdf
- Nanoparticle Inks for Printed Electronics(纳米油墨印刷电子产品).pdf
- Nanotechnology in the Military ICE Home Page(纳米技术在军事冰主页).pdf
- NASA Ames Research Center Active Archive (NASA艾姆斯研究中心活跃归档).pdf
- National GIS Policy of the United Kingdom (国家地理信息系统联合王国的政策).doc
最近下载
- 高等职业学校口腔医学技术专业实训教学条件建设标准.docx VIP
- 《睑板腺功能障碍雷火灸技术操作规范》(发布稿).pdf VIP
- 钛管道施工及验收规范.pdf
- 新能源汽车行业电驱动行业系列专题(一):聚焦3000亿市场,技术迭代推动降本增效-20230308-中信证券-35页.pdf
- 语文课程与教学论考试例题汇编.pdf VIP
- 物流项目管理 物流项目团队组建与管理 2.ppt
- Siemens 西门子工业 RWG Universal Controller RWG Universal Controller 使用手册.pdf
- 达格列净二甲双胍缓释片(I)-临床用药解读.pptx
- 泄殖腔畸形手术.pptx VIP
- TGXAS-睑板腺功能障碍雷火灸技术操作规范编制说明.docx VIP
文档评论(0)