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Homework9-help

Homework9-help - 14.4 Model The air-track glider attached...

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14.4. Model: The air-track glider attached to a spring is in simple harmonic motion. Visualize: The position of the glider can be represented as x ( t ) = A cos ω t . Solve: The glider is pulled to the right and released from rest at 0 s t = . It then oscillates with a period and a maximum speed 2.0 s T = max 40 cm s 0.40 m s v = = . (a) max max 2 2 0.40 m s and rad s 0.127 m 12.7 cm 2.0 s rad s v v A A T π π ω ω π ω π = = = = = = = = (b) The glider’s position at t = 0.25 s is ( ) ( )( ) 0.25 s 0.127 m cos rad s 0.25 s 0.090 m 9.0 cm x π = = = COS wave The graph shows the position x of an oscillating object as a function of time. The equation of the graph is , where A is the amplitude, ω is the angular frequency, and φ is a phase constant. The quantities M, T and N are measurements to be used in your answers. What is A in the equation? A=M What is ω in the equation? 2 π /T What is φ in the equation? 2 π N /T , looked at Figure, when t = -N, x (-N) = M, that is M = M cos(2 π /T*(-N)+ φ ) cos(2 π /T*(-N)+ φ ) =1, 2 π /T*(-N)+ φ =0, so that φ = 2 π N /T 14.14. Model: The oscillating mass is in simple harmonic motion.

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