chapter13 - Chapter 13 Chapter 13 Vibrations and Waves When...

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Unformatted text preview: Chapter 13 Chapter 13 Vibrations and Waves When x is positive , F is negative ; When at equilibrium (x=0), F = 0 ; When x is negative , F is positive ; Hookes Law Reviewed Hookes Law Reviewed F = - Sinusoidal Oscillation Sinusoidal Oscillation Pen traces a sine wave Graphing x vs. t Graphing x vs. t A : amplitude (length, m) T : period (time, s) A T Some Vocabulary Some Vocabulary f = Frequency = Angular Frequency T = Period A = Amplitude = phase x = (- 29 = (2 - 29 = 2 - f = 1 = 2 = 2 Phases Phases Phase is related to starting time 90-degrees changes cosine to sine x = 2 - = 2(- 29 = 2 cos - 2 = ( 29 a x v Velocity is 90 out of phase with x: When x is at max, v is at min .... Acceleration is 180 out of phase with x a = F/m = - (k/m) x Velocity and Velocity and Acceleration vs. time Acceleration vs. time T T T v v and and a a vs. t vs. t Find v max with E conservation Find a max using F=ma x = = - = - 1 2 kA 2 = 1 2 2 = - kx = ma- kA cos wt = - ma max cos wt a max = A k m What is What is ? ? Requires calculus. Since d dt A cos = - = = = k m Formula Summary Formula Summary f = 1 = 2 = 2 x = (- 29 = -(- 29 = - 2 (- 29 = k m Example13.1 Example13.1 An block-spring system oscillates with an amplitude of 3.5 cm. If the spring constant is 250 N/m and the block has a mass of 0.50 kg, determine (a) the mechanical energy of the system (b) the maximum speed of the block (c) the maximum acceleration. a) 0.153 J b) 0.783 m/s 2 Example 13.2 Example 13.2 A 36-kg block is attached to a spring of constant k=600 N/m. The block is pulled 3.5 cm away from its equilibrium positions and released from rest at t=0....
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This note was uploaded on 07/25/2008 for the course PHY 231C taught by Professor Pratt during the Spring '06 term at Michigan State University.

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chapter13 - Chapter 13 Chapter 13 Vibrations and Waves When...

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