problem13_25

University Physics with Modern Physics with Mastering Physics (11th Edition)

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Unformatted text preview: 13.25: a) amax = 2 A = (2f ) 2 A = ( 2(0.85 Hz) ) (18.0 10-2 m) = 5.13 m/s2 . vmax = 2 A = 2fA = 0.961 m/s . b) ax = -(2f ) 2 x = -2.57 m/s 2 , v = (2f ) A2 - x 2 = ( 2 (0.85 Hz) ) (18.0 10- 2 m)2 - (9.0 10- 2 m)2 = 0.833 m/s. c) The fraction of one period is (1 2 ) arcsin (12.0 18.0), and so the time is (T 2 ) arcsin (12.0 18.0) = 1.37 10 -1 s. Note that this is also arcsin ( x A) . 2 2 2 d) The conservation of energy equation can be written 1 kA = 1 mv + 1 kx . We are 2 2 2 given amplitude, frequency in Hz, and various values of x . We could calculate velocity from this information if we use the relationship k m = 2 = 4 2 f 2 and rewrite the conservation equation as 1 2 A2 = 1 v2 2 4 2 f 2 + 1 x 2 . Using energy principles is generally a good 2 approach when we are dealing with velocities and positions as opposed to accelerations and time when using dynamics is often easier. ...
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