1 / 8

Pendulums and Resonance

Pendulums and Resonance. Lecture 3. Pre-reading : §14.5–14.8. SHM: Pendulums. Simple pendulum: point mass on a massless, unstretched string Exhibits SHM with ω = √( g / L ) provided the amplitude (angle) is small (θ≲15°)

ivrit
Télécharger la présentation

Pendulums and Resonance

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. PendulumsandResonance • Lecture 3 Pre-reading: §14.5–14.8

  2. SHM: Pendulums • Simple pendulum: point mass on a massless, unstretched string • Exhibits SHM with ω = √(g/L)provided the amplitude (angle) is small (θ≲15°) • For real pendulum, need to know mass (m), distance to center of massd, and moment of inertiaI about rotation axisω = √(mgd/I)provided the amplitude (angle) is small (θ≲15°) §14.5–14.6

  3. If friction force varies linearly with speed, we can solve for motion: with b describing the amount of damping Damped Oscillations • In real world, friction causes oscillations to decrease in amplitude §14.7

  4. Critical dampingif b=2√(km) ⇒ ωʹ=0 returns to equilibrium without oscillating! • Underdampedb < 2√(km) • Overdampedb > 2√(km) Effects of damping • Amplitude decays exponentially. • Energy decays exponentially. • Angular frequency decreases.

  5. Compare driving frequency with ‘natural frequency’ • If ωd ≃ωʹthen system oscillates with resonant behaviour: amplitude gets very large Forced Oscillations • Now we add a driving force to a damped harmonic oscillator • Suppose driving force is sinusoidal with driving frequency ωd §14.8

  6. Mechanical waves • Read §15.1–15.2 Next lecture

More Related