phy293 - x ) F ( x ) =-sx Hooke sLaw , 1660 , England 2....

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
PHY293 Oscillations Lecture #1 September 11, 2009 1. Introduction/WebSite 2. Why study waves and oscillations? (see slides attached) 3. EKG demonstration ( http://faraday.physics.utoronto.ca/IYearLab/EKG.pdf ) 4. Tacoma Narrows bridge video ( http://www.youtube.com/watch?v=P0Fi1VcbpAI ) Start of material 1. Simple Harmonic Oscillations Linear resorting force Displace mass, m , spring will pull it back Assume F ( x = 0) = 0 , in other words x = 0 is equilibrium position Consider: F ( x ) = - ( sx + s 2 x 2 + s 3 x 3 + ... ) Minus sign is there to ensure the force pushes mass back to equilibrium For small enough displacements, eg: x ± s/s 2 ; p s/s 3 ; etc. We can ignore all but the linear term (this defines “small
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x ) F ( x ) =-sx Hooke sLaw , 1660 , England 2. Equation of Motion Newtons Law: F = ma (1686!, England) Gives us the following: F = ma =-sx Notation x = dx/dt ; x = d 2 x/dt 2 Gives: m x =-sx or m x + sx = 0 Will guess the solution for this second order differential equation x = a cos( t + ) a (Amplitude) and (Phase) are determined from initial conditions (must be two for a second order differential equation). is the oscillation frequency that is uniquely determined by the equations of motion....
View Full Document

Ask a homework question - tutors are online