This preview shows pages 1–6. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Damped Oscillations (Serway 15.615.7) Simple Pendulum L T L g dt d = 2 2 mg Recall, for a simple pendulum we have the following equation of motion: Which give us: L g = Hence: 2 2 2 4 gT g L = = Application  measuring height  finding variations in g underground resources or: 2 2 2 4 T L L g = = t x x t SHM : x(t) = A cos t Motion continues indefinitely. Only conservative forces act, so the mechanical energy is constant. Damped oscillator : dissipative forces (friction, air resistance, etc. ) remove energy from the oscillator, and the amplitude decreases with time. SHM and Damping ) cos( ) ( 2 + = t Ae t x t m b For weak damping (small b ), the solution is: f =  b v where b is a constant damping coefficient x t A damped oscillator has external nonconservative force(s) acting on the system. A common example is a force that is proportional to the velocity. eg: green water (weak damping) A e(b/2m)t 2 2 dt x d m dt dx b kx = F=ma give: Without damping: the angular frequency is 2 2 2 2 2  =...
View
Full
Document
This note was uploaded on 10/14/2011 for the course ENGINEER CHEM ENG 3 taught by Professor Ghosh during the Spring '11 term at McMaster University.
 Spring '11
 Ghosh

Click to edit the document details