SUMMARY The goal of Chapter 14 has been to understand systems that oscillate with simple harmonic motion. General Principles Dynamics SHM occurs when a linear restoring force acts to return a system to an equilibrium position. Horizontal spring Vertical spring The origin is at the equilibrium position Pendulum v5 Å g L T 5 2 p Å L g ( F net ) t 52 1 mg L 2 s v5 Å k m T 5 2 p Å m k ( F net ) y 52 ky D L 5 mg / k . ( F net ) x 52 kx Energy If there is no friction or dissipation, kinetic and potential energy are alternately transformed into each other, but the total mechanical energy is conserved. In a damped system, the energy decays exponentially where is the time constant . t E 5 E0 e 2 t / t 5 1 2 kA 2 5 1 2 m ( v max ) 2 E 5 1 2 mv x 2 1 1 2 kx 2 E 5 K 1 U Important Concepts Simple harmonic motion (SHM) is a sinusoidal oscillation with period T and amplitude A . Frequency Angular frequency Position Velocity with maximum speed Acceleration a x 52v 2 x v max 5v A v x ( t
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This note was uploaded on 09/26/2010 for the course PHYS 021 taught by Professor Dick during the Spring '08 term at GWU.