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1. A) Write down Newton's second law for a damped harmonic oscillator and identify the terms. B) Assume a general solution: x(t) = exp{-at} [ASin(@t) +BC0S(@t)], and describe in one sentence how we solve for a and @. Simply state the answer for these two variables. C) Assume a spring constant of 4.00-N/m and a mass of 4.00-kg and determine what is required for CRITICALLY damped motion. Graph x(t) if x(0) = 10 cm and it is at rest for this critically damped case.

1. A) Write down Newton's second law for a damped harmonic oscillator and identify the terms. B) Assume a general solution: x(t) = exp{-at} [ASin(@t) +BC0S(@t)], and describe in one sentence how we solve for a and @. Simply state the answer for these two variables. C) Assume a spring constant of 4.00-N/m and a mass of 4.00-kg and determine what is required for CRITICALLY damped motion. Graph x(t) if x(0) = 10 cm and it is at rest for this critically damped case.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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1. A) Write down Newton's second law for a damped harmonic oscillator and identify the terms. B) Assume a general solution: x(t) = exp{-at} [ASin(@t) +BCos(@t)], and describe in one sentence how we solve for a and o. Simply state the answer for these two variables. C) Assume a spring constant of 4.00-N/m and a mass of 4.00-kg and determine what is required for CRITICALLY damped motion. Graph x(t) if x(0) = 10 cm and it is at rest for this critically damped case.
Transcribed Image Text:1. A) Write down Newton's second law for a damped harmonic oscillator and identify the terms. B) Assume a general solution: x(t) = exp{-at} [ASin(@t) +BCos(@t)], and describe in one sentence how we solve for a and o. Simply state the answer for these two variables. C) Assume a spring constant of 4.00-N/m and a mass of 4.00-kg and determine what is required for CRITICALLY damped motion. Graph x(t) if x(0) = 10 cm and it is at rest for this critically damped case.
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