OSCILLATIONS

OSCILLATIONS - cos x t A t ϖ = 29 29 29 2 2 2 cos d x t a t dt a t A t = =-23 Vertical Oscillations s F w k L mg = ∆ = 24 29 29 cos y t A t ϖ

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1 Oscillations take place about an equilibrium position. Simple Harmonic Motion
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2 OSCILLATIONS Vertical Horizontal
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3 Simple Harmonic Motion
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4 VERTICAL OSCILLATIONS
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5 Simple Harmonic Motion The time to complete one full cycle, or one oscillation, is called the period of the motion. “T” – units: seconds
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6 Simple Harmonic Motion
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7
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8 ( 29 cos 2 x t A f t π   =  ÷  
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9 Angular Frequency
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10 Velocity in SHM
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11 SHM and Circular Motion
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SHM and Circular Motion 12
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13 The Phase Angle
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14 The Phase Angle Phase Angle
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15 Initial Conditions
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16
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17 The Dynamics of SHM
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18 2 2 1 1 2 2 E mv kx = + ENERGY in SHM
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19
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20 ENERGY in SHM 2 1 2 E at x A U kA = ± = = ÷ 2 max 1 0 2 E at x K mv = = = ÷ 2 2 max max 1 1 2 2 k mv kA v A m = =
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21 Frequency in SHM max max k v A k m m v A ϖ = = = 2 2 m T T k π = = 1 2 k and f m =
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22 ( 29
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Unformatted text preview: cos x t A t ϖ = ( 29 ( 29 ( 29 2 2 2 cos d x t a t dt a t A t = = -23 Vertical Oscillations s F w k L mg = ∆ = 24 ( 29 ( 29 cos y t A t ϖ φ = + 25 The Pendulum A mass m attached to a string of length L and free to swing back and forth. 26 The Pendulum ( 29 ( 29 max cos t t θ ϖ φ = + 2 g f L π = = Restoring Force. 27 28 Damped Oscillations ( 29 ( 29 2 cos bt m D bv x t Ae t ϖ φ-=-= + r r b is called the damping constant 29 2 2 4 k b m m ϖ=-30 Forced Oscillations and Resonance 31 ( 29 max cos d F t F t ϖ = 32 ( 29 dx v t dt = 33 The Dynamics of SHM 34...
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This note was uploaded on 11/13/2011 for the course BRAE 236 taught by Professor Styles during the Fall '08 term at Cal Poly.

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OSCILLATIONS - cos x t A t ϖ = 29 29 29 2 2 2 cos d x t a t dt a t A t = =-23 Vertical Oscillations s F w k L mg = ∆ = 24 29 29 cos y t A t ϖ

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