A weight is attached to a spring suspended vertically from a ceiling. When a driving force is applied to the system, the weight moves vertically from its equilibrium position, and this motion is modeled by =sin(4t) + y = cos(4t) 8 where y is the displacement (in feet) from equilibrium of the weight and t is the time (in seconds). (a) Use the identity a sin(Be) + b cos(Be) = √2 + b2 sin(B8 + C) where Carctan (b/a), a > 0, to write the model in the form y = √² + b2 sin(Bt + C). (Round C to four decimal places.) y = (b) Find the amplitude of the oscillations of the weight. ft (c) Find the frequency of the oscillations of the weight. cycle per second
A weight is attached to a spring suspended vertically from a ceiling. When a driving force is applied to the system, the weight moves vertically from its equilibrium position, and this motion is modeled by =sin(4t) + y = cos(4t) 8 where y is the displacement (in feet) from equilibrium of the weight and t is the time (in seconds). (a) Use the identity a sin(Be) + b cos(Be) = √2 + b2 sin(B8 + C) where Carctan (b/a), a > 0, to write the model in the form y = √² + b2 sin(Bt + C). (Round C to four decimal places.) y = (b) Find the amplitude of the oscillations of the weight. ft (c) Find the frequency of the oscillations of the weight. cycle per second
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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