# lecture35 - Damped Oscillations (Serway 15.6-15.7) Simple...

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Unformatted text preview: Damped Oscillations (Serway 15.6-15.7) 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 - =...
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## 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.

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lecture35 - Damped Oscillations (Serway 15.6-15.7) Simple...

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