free_oscillators - k m kx Free Oscillators: Consider the...

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-kx m k Free Oscillators: Consider the simple system shown above. Use the “force” method to find its equation of motion. Σ F x = ma x - kx = m d 2 x dt 2 0 = d 2 x dt 2 + k m x Since we know this thing is going to oscillate (move back and forth in a periodic manner) let’s try a solution that looks like: x ( t ) = A cos( ωt + δ ) Terminology: A is the amplitude . It corresponds to the maximum displacement from equilibrium the object in simple harmonic oscillation experiences, and is almost always taken to be positive. A is determined by the initial conditions of the problem. ωt + δ is the phase . It’s the angular argument to the cosine function and must be expressed in radians. δ is the phase shift . This is the phase of the system at the time t = 0. δ is determined (not surprisingly) by the initial conditions of the problem. 1
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ω is the angular frequency . Think of this as the conversion factor be- tween time and phase: ω = 2 π T , where 2 π
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This note was uploaded on 11/12/2010 for the course PHYSICS 1B 318007241 taught by Professor Corbin during the Spring '10 term at UCLA.

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free_oscillators - k m kx Free Oscillators: Consider the...

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