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# HW9 - PHYS 3202 Classical Mechanics II Homework#9 Due at...

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PHYS 3202 Classical Mechanics II - Homework #9 Due at 12:05pm, Friday April 15, 2011 in the class Please show intermediate steps of your calculations. If necessary, you may draw diagram(s). Problem 1 (10 points): Two identical massless springs with spring constant κ each and two particles of mass m each are connected in an array. Spring 1 connects a ﬁxed wall and particle 1, spring 2 connects particle 1 and particle 2. Particle 1 is in the middle. Let the displacement of the j -th particle from its equilibrium point be q j . Find the characteristic frequencies of the system. Omit gravity. If q 1 (0) = 0 , q 2 (0) = ±, ˙ q 1 (0) = ˙ q 2 (0) = 0 , ﬁnd q 1 ( t ) and q 2 ( t ) as functions of the time t . Problem 2 (10 points): n identical springs, with spring constant κ each, and n particles of mass m each are connected in a linear array: spring 1 connects a ﬁxed wall and particle 1, spring j connects particle j - 1 and particle j , where j = 2 , ··· ,n . The

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HW9 - PHYS 3202 Classical Mechanics II Homework#9 Due at...

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