5_6-Clickers-Damped Oscillators

# 5_6-Clickers-Damped Oscillators - Damped oscillations 1 The...

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1 Damped oscillations

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The ODE for damped simple harmonic motion is: A) α,β>0 B) α,β<0 C) α<0, β>0 D) α>0, β<0 E) Depends! 2 d 2 y dt 2 + 2 β dy dt + α y = 0 What are the signs of the constants α and β?
For a mass on a spring, with damping: with k, b>0. The ODE for damped simple harmonic motion is: A) α,β>0 B) α,β<0 C) α<0, β>0 D) α>0, β<0 E) Depends! 3 d 2 y dt 2 + 2 β dy dt + α y = 0 F =- k x - b Ý x What are the signs of the constants α and β?

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4 What are the roots of the auxiliary equation D2 + D - 2 = 0 ? A) 1 and 2 B) 1 and -2 C) -1 and 2 D) -1 and -2 E) Other/not sure. ..
5 What are the roots of the auxiliary equation y’’(t) +y(t) = 0 ? A) 1 and -1 B) 1 and 0 C) just 1 D) just i E) i and -i

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6 A particle oscillates in a one-dimensional potential. How many (which?) of the following properties guarantee simple harmonic motion? i) The period T is independent of the amplitude A ii) The potential U(x)~x2 iii) The force F=–kx (Hooke’s law) iv) The position is sinusoidal in time: x=Asin(wt+a) A) only 1 of these properties guarantees simple harmonic motion B) exactly 2 properties guarantee simple harmonic motion C) exactly 3 properties guarantee simple harmonic motion D) all (any one of these guarantees simple harmonic motion)
7 A mass on a spring has a small damping term added. When it passes through x=0, which is correct? A) The mass is instantaneously speeding up B) The mass is instantaneously slowing down C) The mass is at a maximum speed (and is thus neither speeding up nor slowing down D) The answer depends on which WAY it is passing through the origin.

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## This note was uploaded on 02/27/2012 for the course PHYSICS 2210 taught by Professor Stevepollock during the Spring '11 term at Colorado.

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5_6-Clickers-Damped Oscillators - Damped oscillations 1 The...

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