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Unformatted text preview: Homework 9 Chapt. 14 solutions (1) Cosine Wave The graph shows the position of an oscillating object as a function of time . The equation of the graph is , Part A What is A in the equation? Part B What is in the equation? Part C What is in the equation? From the figure we see when t = N, x = M Using the cos wave function M = M cos(2 /T * (N) + ) cos(2 /T * (N) + )=1 (2 /T * (N) + ) = 0, = 2 N /T 14.14. Model: The oscillating mass is in simple harmonic motion. Solve: (a) The amplitude A = 2.0 cm. (b) The period is calculated as follows: 2 2 10 rad s 0.628 s 10 rad s T T = = = = (c) The spring constant is calculated as follows: ( ) ( ) 2 2 0.050 kg 10 rad s 5.0 N m k k m m = = = = (d) The phase constant 1 4 rad. =  (e) The initial conditions are obtained from the equations ( ) ( ) ( ) ( ) ( ) ( ) 1 1 4 4 2.0 cm cos 10 and 20.0 cm s sin 10 x x t t v t t = =  At t = 0 s, these equations become ( ) ( ) ( ) ( ) 1 1 4 4 2.0 cm cos 1.414 cm and 20.0 cm s sin 14.14 cm s x x v = = =  = In other words, the mass is at + 1.414 cm and moving to the right with a velocity of 14.14 cm/s. (f) The maximum speed is ( ) ( ) max 2.0 cm 10 rad s 20.0 cm s v A = = = . (g) The total energy ( )( ) 2 2 3 1 1 2 2 5.0 N m 0.02 m 1.0 10 J E kA = = = ....
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 Spring '10
 ZHOU

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