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Unformatted text preview: Chapter 11 Vibrations and Waves Units of Chapter 11 Simple Harmonic Motion Energy in the Simple Harmonic Oscillator The Period and Sinusoidal Nature of SHM The Simple Pendulum 111 Simple Harmonic Motion Any vibrating system where the restoring force is proportional to the negative of the displacement is in simple harmonic motion (SHM), and is often called a simple harmonic oscillator. 111 Simple Harmonic Motion If an object vibrates or oscillates back and forth over the same path, each cycle taking the same amount of time, the motion is called periodic. The mass and spring system is a useful model for a periodic system. Equilibrium position, x=0 ( spring is neither stretched nor compressed) The minus sign on the force indicates that it is a restoring force it is directed to restore the mass to its equilibrium position. k is the spring constant The force is not constant, so the acceleration is not constant either (111) The force exerted by the spring depends on the displacement: 111 Simple Harmonic Motion Displacement X is measured from the equilibrium point Amplitude A is the maximum displacement A cycle is a full toandfro motion; this figure shows half a cycle Period T is the time required to complete one cycle Frequency is the number of cycles completed per second 112 Energy in SHM If the mass is at the limits of its motion, the energy is all potential. If the mass is at the equilibrium point, the energy is all kinetic. (113) The total mechanical energy is 112 Energy in the Simple Harmonic Oscillator The total energy is conserved (114c) (115) =1/2 mv 2 max (d) (c) (b) 111 Simple Harmonic Motion If the spring is hung vertically, the only change is in the equilibrium position, which is at the point where the spring force equals the gravitational force.gravitational force....
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This note was uploaded on 04/27/2009 for the course PHSX 114 taught by Professor Davis during the Spring '08 term at Kansas.
 Spring '08
 DAVIS

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