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Sinusoidal Nature of SHM

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SHM and Uniform Circular Motion

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Horizontal View

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θ x = A cos θ A ω = θ/t x = A cos(ωt) ω = 2П/T = 2Пf

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At what time is there: max. positive acceleration max. negative acceleration max. positive velocity max. negative velocity Equation: y t y = A sin (ωt) ω =2π/T 3T/4 T/4 0 & T T/2

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Period of Mass on Spring Compare to circular motion with same T v = Δx/t v 0 = 2ПA/T T = 2ПA/v 0 ½ mv 0 2 = ½ kA 2 v 0 = A (k/m)T = 2П (m/k)

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To double the period: change in m: 4 times change in k: ¼ as large

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