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PHYS310_Exam2_solutions

PHYS310_Exam2_solutions - PHYS 310 Exam2 Name Problem 1(30...

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Unformatted text preview: PHYS 310: Exam2 October 19, 2011 Name: Problem 1 (30 points). The initial conditions of a two-dimensional isotropic oscillator are as follows: A y x A y A x t ϖ 3 , , 4 , , = = = = = where ϖ is the angular frequency. (a) (20 points) Find x and y as functions of t (b) (5 points) Show that the motion takes place entirely within the rectangle of dimensions 2A and 10A. (5 points) Make a sketch of the path. ( 29 cos x A t ϖ α = + , ( 29 sin x A t ϖ ϖ α = - + from x = o , α = from x A = o , cos x A t ϖ = ( 29 cos y B t ϖ β = + , ( 29 sin y B t ϖ ϖ β = - + 2 2 2 1 1 1 2 2 2 kB ky my = + o o with 4 y A = o , 3 y A ϖ = o and k m ϖ = : ( 29 2 2 2 2 2 2 1 16 9 25 B A A A ϖ ϖ = + = 5 B A = Then 4 5 cos A A β = and 3 5 sin A A ϖ ϖ β = - 1 1 4 3 cos sin 36.9 5 5 β-- = =- = - o ( 29 5 cos 36.9 y A t ϖ =- o Since maximum x and y displacements are A ± and 5 A ± , respectively, the motion takes place entirely within a...
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PHYS310_Exam2_solutions - PHYS 310 Exam2 Name Problem 1(30...

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