This preview shows page 1. Sign up to view the full content.
Unformatted text preview: m d 2 x dt 2 + kx = A cos( 1 t ) , where m is the mass, k is the springs constant (cfr Hookes law). The external force is periodic with amplitude A > 0 and frequency 1 / 2 . If there is no external forcing ( A = 0), we get a harmonic oscillator with natural frequency / 2 , where = r k/m . Show that the general solution y g ( t ) is bounded if 1 n = (a function f ( t ) is called bounded if there is some positive constant K so that  f ( t )  < K for all t .), but that y g ( t ) is not bounded if 1 = . This last case is a typical example of what is known as a resonance phenomenon . Such phenomena may occur when a frequency of an external forcing term matches a natural frequency of the unforced system. 5. Find the general solution to the system dx dt = x + y dy dt = 2 x + y * MAP 2302; Instructor: Patrick De Leenheer. 1...
View
Full
Document
This note was uploaded on 09/12/2011 for the course MAP 4305 taught by Professor Deleenheer during the Summer '06 term at University of Florida.
 Summer '06
 DeLeenheer

Click to edit the document details