Homework 31

# Homework 31 - homework 31 BAUTISTA, ALDO Due: Apr 17 2006,...

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1 Version number encoded for clicker entry: V1:1, V2:4, V3:2, V4:4, V5:3. Question 1 Part 1 of 3. 10 points. A 1 . 7 kg object oscillates with an initial am- plitude of 179 cm on a spring of force constant 539 . 5 N / m. Find the period. Correct answer: 0 . 352703 s (tolerance ± 1 %). Explanation: Let : m = 1 . 7 kg and k = 539 . 5 N / m . The period of the oscillator is T = 2 π r m k = 2 π s 1 . 7 kg 539 . 5 N / m = 0 . 352703 s . Question 2 Part 2 of 3. 10 points. Find the total initial energy. Correct answer: 864 . 306 J (tolerance ± 1 %). Explanation: Let : A = 179 cm = 1 . 79 m . The initial energy is E 0 = 1 2 k A 2 = 1 2 (539 . 5 N / m)(1 . 79 m) 2 = 864 . 306 J . Question 3 Part 3 of 3. 0 points. If the energy decreases by 1 percent per period, ±nd the damping constant b . Correct answer: 0 . 0481993 kg / s (tolerance ± 1 %). Explanation: Let : | Δ E | E = 0 . 01 , m = 1 . 7 kg , and T = 0 . 352703 s . Relating the fractional rate at which the en- ergy decreases, Q = 2 π ± | Δ E | E ² cycle = 2 π 0 . 01 . Express the Q value in terms of b : Q = ω 0 m b = 2 π 0 . 01 b = 0 . 01 ω 0 m 2 π = 0 . 01 (2 π ) m 2 π T = 0 . 01 m T = 0 . 01 (1 . 7 kg) 0 . 352703 s = 0 . 0481993 kg / s . Question 4 Part 1 of 2. 10 points. Waves of frequency 199 Hz and amplitude 0 . 5 cm move along a 19 . 3 m string that has a mass of 0 . 021 kg and a tension of 50 N. What is the average total energy of the waves on the string? Correct answer:

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## This note was uploaded on 10/13/2009 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas.

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Homework 31 - homework 31 BAUTISTA, ALDO Due: Apr 17 2006,...

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