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An oscillating spring has a frequency of 1.16 Hz (here is some information about the frequency unit Hertz) and amplitude 3 centimeters. You are testing the damping effect of a frictional force on the spring, and find that it reduces the frequency to 0.73 Hz and the amplitude to 2.1 centimeters. You want to model this behavior with a piecewise function of the form: Α Cos(2 πω) 1) , A2 cos(2rort + C), t> 5 0

An oscillating spring has a frequency of 1.16 Hz (here is some information about the frequency unit Hertz) and amplitude 3 centimeters. You are testing the damping effect of a frictional force on the spring, and find that it reduces the frequency to 0.73 Hz and the amplitude to 2.1 centimeters. You want to model this behavior with a piecewise function of the form: Α Cos(2 πω) 1) , A2 cos(2rort + C), t> 5 0

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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An oscillating spring has a frequency of 1.16 Hz (here is some information about the frequency. unit Hertz) and amplitude 3 centimeters. You are testing the damping effect of a frictional force on the spring, and find that it reduces the frequency to 0.73 Hz and the amplitude to 2.1 centimeters. You want to model this behavior with a piecewise function of the form: 0 <t < 5 f(t) = { Aj cos(2x0, t), A2 cos(2rwzt + C), t> 5 Here each value of A represents an amplitude and each value of @ ("omega") represents a frequency. (It may help to recall that the period of a sinusoidal function is the length of time for one cycle to occur, so frequency and period have a reciprocal relationship, and that the function 2л A cos(Bt) has period 4 when interpreting the pieces of this function.) Find the value of the parameter C that makes the piecewise function continuous at t = C controls the horizontal shift of a sinusoidal function; this shifts the t = 0 point to t = -. 10. (Recall This will help with interpretation, but you should be able to algebraically solve for C even if this interpretation isn't clear at first.) Use the limit definition of continuity in your computation, and be sure to tell the story of your thought process - how you choose each limit computation you do.
Transcribed Image Text:An oscillating spring has a frequency of 1.16 Hz (here is some information about the frequency. unit Hertz) and amplitude 3 centimeters. You are testing the damping effect of a frictional force on the spring, and find that it reduces the frequency to 0.73 Hz and the amplitude to 2.1 centimeters. You want to model this behavior with a piecewise function of the form: 0 <t < 5 f(t) = { Aj cos(2x0, t), A2 cos(2rwzt + C), t> 5 Here each value of A represents an amplitude and each value of @ ("omega") represents a frequency. (It may help to recall that the period of a sinusoidal function is the length of time for one cycle to occur, so frequency and period have a reciprocal relationship, and that the function 2л A cos(Bt) has period 4 when interpreting the pieces of this function.) Find the value of the parameter C that makes the piecewise function continuous at t = C controls the horizontal shift of a sinusoidal function; this shifts the t = 0 point to t = -. 10. (Recall This will help with interpretation, but you should be able to algebraically solve for C even if this interpretation isn't clear at first.) Use the limit definition of continuity in your computation, and be sure to tell the story of your thought process - how you choose each limit computation you do.
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