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Unformatted text preview: M341 H5 (S. Zhang) 3.4. 1. EP 3.4: 1, 3, 5, 14, 15, 18, 32, 33 ans: 2. Determine the period and frequency of the simple har monic motion of a 4kg mass on the end of a pring with spring constant 16N/m. ans: ( ) EP 3.4: 1 Freqency = r k m = r 48 . 75 = 8 rad sec = 4 Hz Period T = 2 = 4 sec 3. A mass of 3kg is attached the end of a pring that is stretched 20 cm by a force of 15 N. It is set in motion with initial position x = 0 and initial velocity v = 10m/s. Find the amplitude, period, and frequency of the resulting motion. ans: ( ) EP 3.4: 3 The spring constant k = 15 / . 2 = 75 N/m The solution for 3 x 00 + 75 x = 0 , x (0) = 0 , x (0) = 10 is x ( t ) = 2 sin 5 t The amlitude is 2 m; the frequency is = r k m = 5 rad/sec = 2 . 5 Hz The period is T = 2 5 sec 4. Assume that the equation for a simple pendulum of length L is L 00 + g = 0 where g = GM/R 2 . Two pendulums are of lengths L 1 and L 2 and when located at the respetive distances R 1 and R 2 from the center of the earth having periods p 1 and p 2 . Show that p 1 p 2 = R 1 L 1 R 2 L 2 ans: ( ) EP 3.4: 5 When small, the equation for a pendulum is...
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This note was uploaded on 04/07/2008 for the course MATH 341 taught by Professor Zhang during the Fall '08 term at University of Delaware.
 Fall '08
 Zhang
 Linear Algebra, Algebra, Equations

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