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Published bySteven Wade Modified over 9 years ago
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Simple Harmonic Motion
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Ideal Springs F Applied =kx k = spring constant x = displacement of the spring +x pulled displacement -x compressed displacement
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Hooke’s Law Describes the restoring force of an ideal spring F = -kx Negative sign indicates that this force always goes in the opposite direction of displacement
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Hooke’s Law This type of restoring force will create a back and forth or up and down type of motion This type of friction-free motion is designated simple harmonic motion The maximum excursion from equilibrium is the amplitude A
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Period Mass-Spring Complex T = 2π√(m/k) Pendulum T = 2π√(L/g)
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The Reference Circle Simply a ball moving in uniform circular motion The shadow cast by the ball on a film creates the same type of sinusoidal pattern It makes another model of simple harmonic motion
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Displacement x = A cos = A cos t = 2 / T f = 1 / T = 2 f ( is often called angular frequency)
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Velocity & Acceleration v = -A sin = -A sin t v max = A a = -A 2 cos = - 2 cos t a max = A 2
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Frequency of Vibration = (k / m) 1/2 must be in radians per second k spring constant m mass
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Energy & Simple Harmonic Motion W elastic = ½ kx o 2 – ½ kx f 2 PE elastic = ½ kx 2 E Total = ½ mv 2 + ½ 2 + mgh + ½ kx 2
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