# Lect_27 - Lecture 27 The Pendulum Damped and Forced...

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Lecture 27 The Pendulum Damped and Forced Oscillations ACT: Energy oscillations A mass m = 5 kg oscillates at the end of a spring of constant k = 2000 N/m. At t = 0, its acceleration is maximum. How long will it take before the potential energy reaches its next maximum? A. 0.31 s B. 0.16 s C. 0.08 s To get to the next peak in U , it takes half a period 12 0.16 s 22 Tm π ω == = At = 0: Max a Max x Max U x T The simple pendulum The simple pendulum L R c b s θ θθ = sin cos bc RR A mass m is suspended at the end of a massless string of length . Find the frequency of the oscillations for small displacements. Small ± ± bs cR sin cos 1 Small

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θ L The oscillations are rotations about point P. τ τθ == net sin g mgL −= 2 2 2 sin d mL dt Newton’s second law: ( ) α = net I T mg P += 2 2 0 SHM θω ϕ ω =+ = 0 cos( ) with t Solution: 2 2 2 Small DEMO: Pendulum The physical pendulum The physical pendulum = a rigid body that oscillates about an axis (P). CM ( ) = net 2 2 sin mgd Oscillations about P: f s N P + = 2 2 sin 0 + = 2 2 0 For small : = 2 SHM with Distance between CM and
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## This note was uploaded on 04/16/2008 for the course PHYSICS 221 taught by Professor Johnson during the Fall '06 term at Iowa State.

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Lect_27 - Lecture 27 The Pendulum Damped and Forced...

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