OSCILLATIONS

# OSCILLATIONS - cos x t A t ϖ = 29 29 29 2 2 2 cos d x t a...

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1 Oscillations take place about an equilibrium position. Simple Harmonic Motion

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2 OSCILLATIONS Vertical Horizontal
3 Simple Harmonic Motion

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4 VERTICAL OSCILLATIONS
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
7

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8 ( 29 cos 2 x t A f t π   =  ÷  
9 Angular Frequency

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10 Velocity in SHM
11 SHM and Circular Motion

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SHM and Circular Motion 12
13 The Phase Angle

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14 The Phase Angle Phase Angle
15 Initial Conditions

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16
17 The Dynamics of SHM

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18 2 2 1 1 2 2 E mv kx = + ENERGY in SHM
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 = =
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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OSCILLATIONS - cos x t A t ϖ = 29 29 29 2 2 2 cos d x t a...

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