# q04 - a which can be represented by a series of harmonic...

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Physics 3221 Mechanics I Fall Term 2010 Quiz 4 This is a 15 min. quiz (closed book). There are two problems (the second one is on the back). M 30 M 20 M 10 0 10 20 30 M 2 M 1 0 1 2 t x L t R Figure 1: An illustration for Problem 1. Problem 1. [2 pts] The graph above shows the response of: (A) a damped oscillator to an impulse forcing function (B) an undamped oscillator to an impulse forcing function (C) a damped oscillator to a step forcing function (D) an undamped oscillator to a step forcing function (E) This is a trick question. This oscillator is not responding.

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Problem 2. A damped linear oscillator is subjected to the periodic forcing function F ( t ) = - F 0 , if - 2 a t < - a, + F 0 , if - a t < + a, - F 0 , if + a t < +2
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Unformatted text preview: a. which can be represented by a series of harmonic terms F ( t ) = 1 2 a + ∞ s n =1 ( a n cos nωt + b n sin nωt ) , where a n = ω π i + π/ω − π/ω F ( t ′ ) cos nωt ′ dt ′ = 2 τ i τ F ( t ′ ) cos nωt ′ dt ′ b n = ω π i + π/ω − π/ω F ( t ′ ) sin nωt ′ dt ′ = 2 τ i τ F ( t ′ ) sin nωt ′ dt ′ [1 pt] What is the value of ω in terms of a ? (A) 1 2 a (B) 1 4 a (C) π a (D) π 2 a (E) π 4 a [1 pt] What is the value of a ? (A) 0 (B) F (C)-F (D) 2 F (E)-2 F [1 pt] What is the value of b 1 ? (A) 0 (B) F (C)-F (D) 2 F (E)-2 F...
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q04 - a which can be represented by a series of harmonic...

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