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lecture32 - Oscillatory Motion Serway Jewett(Chapter 15 M...

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Oscillatory Motion Serway & Jewett (Chapter 15)
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M Equilibrium position: no net force M The spring force is always directed back towards equilibrium (hence called the ‘ restoring force ’). This leads to an oscillation of the block about the equilibrium position. M For an ideal spring, the force is proportional to displacement . For this particular force behaviour, the oscillation is simple harmonic motion. x F = -kx
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) cos( φ ϖ + = t A x SHM: x ( t ) t A -A T A = amplitude φ = phase constant ϖ = angular frequency A is the maximum value of x ( x ranges from + A to - A ). φ gives the initial position at t=0: x(0) = A cos φ . ϖ is related to the period T and the frequency f = 1/T T (period) is the time for one complete cycle (seconds). Frequency f (cycles per second or hertz , Hz) is the number of complete cycles per unit time.
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2 2 f T π π ϖ = = units: radians/second or s -1 ϖ (“omega”) is called the angular frequency of the oscillation.
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Velocity and Acceleration 2 MAX MAX 2 2 : Note ) cos( ) ( ) sin( ) ( ) cos( ) ( ϖ ϖ ϖ ϕ ϖ ϖ ϕ ϖ ϖ ϕ ϖ A a A v x t A dt
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