MATH 251 Midterm: MATH 251 PSU s251Exam 2(fa03)
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Solution key: (5 points) a spring-mass system, subject to an external force of 10 cos(2t) newtons, is equipped with a spring with a hooke"s constant 12 newtons per meter. For what mass will the resonance occur? (a) 2 kg (b) 3 kg correct (c) 6 kg (d) 10 kg. Solution: the frequency of free oscillation is subject to the following relation: Solution: the characteristic equation, associated with the homogeneous part of the equation, has root 2 of multiplicity 2. Therefore the solution-to-be has the e2t term multiplied by t2. 2 = 4x1 4x2 x (d) (x . Solution: we think of x1 as y and x2 as y : (5 points) which of the following functions corresponds to this graph: t. 1 (a) tu1(t) 1 (b) tu1(t 1) 1 (c) (t 1)u1(t) 1 correct (d) (t 1)u1(t 1) 1. Solution: we are "turning" at t = 1, that"s why we must have u1(t) term.
