28 - Oscillations

28 - Oscillations - Oscillations Read: 16.1-16.3 HW:...

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Oscillations Read: 16.1-16.3 HW: handout, problems 12, 14, & 16

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Review mathematics ( ) cos xA t + ϕ amplitude phase angle ω is determined by the properties of the system A and ϕ are determined by initial conditions
Velocity ( ) cos xA t + ϕ () sin dx vA t dt == ω ω + ϕ • Velocity is 90 ° out of phase with the displacement -- leads v is zero when x is an extremum v is maximum when x = 0 max = ω

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Acceleration ( ) cos xA t + ϕ ( ) sin vA t =−ω ω +ϕ () 2 cos dv aA t dt == ω ω + ϕ • Acceleration is 180 ° out of phase with the displacement a is zero when x = 0 a is maximum when x is maximum 2 max = ω

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Example A mass ( m = 2 kg) on a spring ( k = 72 N/m) is pulled out 20 cm and released. What is the angular frequency? 2 0.95 s T π == ω 72 N/m 6 rad/s 2 kg k m ω=
Example A mass ( m = 2 kg) on a spring ( k = 72 N/m) is pulled out 20 cm and released. What are the amplitude and phase angle? ( ) cos xA t + ϕ 0: 0.2 m cos tA = ( ) sin vA t =−ω ω +ϕ 0: 0 sin = ϕ 0& 0 . 2 m A ⇒ϕ= = ( ) ( ) 0.2 m cos 6 rad/s xt =

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Example A mass ( m = 2 kg) on a spring (
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This note was uploaded on 04/13/2008 for the course PHYS 211 taught by Professor Shannon during the Spring '08 term at MSU Bozeman.

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28 - Oscillations - Oscillations Read: 16.1-16.3 HW:...

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