A Look at Damped Harmonic Oscillators through the Phase Plane

Autor/inn/en	Daneshbod, Yousef; Latulippe, Joe
Titel	A Look at Damped Harmonic Oscillators through the Phase Plane
Quelle	In: Teaching Mathematics and Its Applications: An International Journal of the IMA, 30 (2011) 2, S.62-69 (8 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0268-3679
DOI	10.1093/teamat/hrr004
Schlagwörter	Motion; Calculus; Mathematics Instruction; Mathematics Education; Equations (Mathematics); Algebra; Mathematical Formulas + Suchen Sie Ihr Suchwort? Bewegungsablauf; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Mathematics lessons; Mathematikunterricht; Mathematische Bildung; Equations; Mathematics; Gleichungslehre; Mathematische Formel
Abstract	Damped harmonic oscillations appear naturally in many applications involving mechanical and electrical systems as well as in biological systems. Most students are introduced to harmonic motion in an elementary ordinary differential equation (ODE) course. Solutions to ODEs that describe simple harmonic motion are usually found by investigating the roots of a corresponding characteristic polynomial and ultimately written out as a time series to be graphed. Although this approach is standard, students often fail to connect the relationship between position and velocity that one achieves using phase plane analysis. The purpose of this article is to illustrate how the phase plane analysis and transformations can be used to gain a deep understanding of damped harmonic oscillations. (As Provided).
Anmerkungen	Oxford University Press. Great Clarendon Street, Oxford, OX2 6DP, UK. Tel: +44-1865-353907; Fax: +44-1865-353485; e-mail: jnls.cust.serv@oxfordjournals.org; Web site: http://teamat.oxfordjournals.org/
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10