Lecture 15 - Resonance

# Lecture 15 - Resonance - Resonance dx m 2 = −kx dt 2 dx m...

This preview shows pages 1–16. Sign up to view the full content.

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Resonance dx m 2 = −kx dt 2 dx m 2 = −kx dt x = A cos ωt + B sin ωt 2 dt x = A cos ωt + B sin ωt m dx 2 2 = − kx ω= 2 k T= m 2π ω Fd = −bv dx = −b dt dx dx m 2 = − kx − b dt dt 2 x = Ce cos ωt Transient solution −α t x = A sin ωt + B cos ωt [ [ L] sin ωt + [ L] cos ωt = 0 ω = ω −α 2 0 2 0 2 k where ω = m b and α = 2m 2 2 ω0 = α is critical damping Forced Oscillations Fex cos ωt dx m 2 = −kx + Fex cos ωt dt x = A cos ωt 2 ( ω − ω 2 0 2 ) A − a cos ωt = 0 0 Fex where a 0 = m a0 A= 2 2 ω0 − ω Damped forced oscillations dx dx Fex cos ωt − kx − b = m 2 dt dt x = A cos ωt + B sin ωt 2 [ L] cos ωt + [ L] sin ωt = 0 A= (ω (ω a0 ( ω − ω 2 0 2 0 2 −ω 22 ) ) ) 2 2 +β ω B= −a0 βω 2 0 −ω 22 +β ω 2 2 Fex where a0 = m b and β = m ...
View Full Document

## This note was uploaded on 11/20/2009 for the course PH ASF taught by Professor Goodstein during the Spring '07 term at Caltech.

### Page1 / 16

Lecture 15 - Resonance - Resonance dx m 2 = −kx dt 2 dx m...

This preview shows document pages 1 - 16. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online