PHYS 422 Lecture 18 Coupled Oscillations and Normal Modes I

PHYS 422 Lecture 18 Coupled Oscillations and Normal Modes I...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
l d O ill ti d Coupled Oscillations and ormal Modes I Normal Modes I
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Coupled Pendulums so far we have restricted ourselves to systems with one type of vibration characterized by a single natural frequency ω 0 real physical systems may have multiple modes of vibration with many different resonant frequencies x B x A
Background image of page 2
Coupled Pendulums let’s consider our prototype system in the following configuration spring is at its laxed length relaxed length no force on A or B x B x A s C t each pendulum oscillates at its natural frequency ω 0 ( ω 0 2 = g/ l ) 0 0 cos cos A B xC x Ct ω = = normal mode of the system
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Coupled Pendulums now let’s put our prototype into the following state coupling spring is stretched half a cycle later it is compressed x B x A exerts forces on both A and B if the pendula were free restoring force m ω 2 0 x spring is stretched (compressed) distance 2x 2kx 2 2 0 2 20 A AA dx mm x k x dt ω ++ = 2 22 2 0 2 ( 2 ) 0 A cA c k x dt m ωω + += =
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/23/2011 for the course PHYS 422 taught by Professor Staff during the Spring '08 term at Purdue.

Page1 / 11

PHYS 422 Lecture 18 Coupled Oscillations and Normal Modes I...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online