sy19_nov07_07hc

sy19_nov07_07hc - ! What do all harmonic oscillations have...

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Unformatted text preview: ! What do all harmonic oscillations have in common? A position of equilibrium A restoring force, which must be linear ( F = -kx ; F = mg is only linear for small angles : sin ! = ! =s/L In this limit we have: F = -ks with k = mg/L ) Inertia The resistive forces are reasonably small Simple Harmonic Motion More tools: Position, velocity, acceleration Energy Damping Simple Harmonic Motion "# $ least friction " = 0.066 sec most friction " = 0.011 sec Damped oscillations of same system : resonance curves for different amount of friction width of res curve at half max more friction - wider res curve less friction narrower resonance curve frequency (Hz) of external force (push or driving force) amplitude of oscillation natural frequency width of resonance curve and damping time: inverse relation " f # $ = ln(2 3 )/ % & 0.4 % Examples: 1. Sitar (Northern India) 7 strings + 11 sympathetic strings Examples: 1. Sitar (Northern India) 7 strings + 11 sympathetic strings 2. Marimba &...
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sy19_nov07_07hc - ! What do all harmonic oscillations have...

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