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aaaTAM203_All_Old_Exams

# aaaTAM203_All_Old_Exams - Your Name T&AM 203 Tuesday Final...

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1)(20 pts) Spring mass. a) (5 pts) Find the equation of motion, a differential equation, for the variable x in the system above. Your differential equation can contain x , its time derivatives, m, c, k, and 0 (Please read item (b) on the cover page.) b) (5 pts) Assume c = 0, x ( t = 0) = d , and ˙ x ( t = 0) = 0. What is ˙ x at time t (answer in terms of some or all of m, k, ℓ 0 , d, and t . c) (5 pts) Assume relatively large c ( c 2 > 4 km ), x ( t = 0) = d , and ˙ x ( t = 0) = 0. Find x ( t ) (or write code that would find x ( t )). d) (5 pts) Whether or not you have succeeded at part (c) above, make a clear plot of x vs t for the conditions in part (c) above.
(work for problem 1, cont’d.)

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2)(20 pts) Car on a ramp. A junior level engineering design course asks students to build a cart (mass = m c ) that rolls down a ramp with angle θ . A small weight (mass m w m c ) is placed on top of the cart on a surface tipped with respect to the cart (angle φ ). Assume the small mass does not slide. Assume massless wheels with frictionless bearings a) (5 pts) Find the acceleration of the cart. Answer in terms of some or all of
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