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1. Answer the following questions. Be sure to show your work. 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 1 1 y=sin 2t+cos 2t where y is the distance from equilibrium (in feet) and t is the time (in seconds). a. Use the identity a- sinBO + bcos BO = √√a² + b².sin(Bt + C) where C = arctan (2), a > 0, to write the model in the form y = √² + b² . sin(Bt + C). b. State the amplitude of the oscillations of the weight. c. Find the frequency of the oscillations of the weight.

1. Answer the following questions. Be sure to show your work. 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 1 1 y=sin 2t+cos 2t where y is the distance from equilibrium (in feet) and t is the time (in seconds). a. Use the identity a- sinBO + bcos BO = √√a² + b².sin(Bt + C) where C = arctan (2), a > 0, to write the model in the form y = √² + b² . sin(Bt + C). b. State the amplitude of the oscillations of the weight. c. Find the frequency of the oscillations of the weight.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 74E
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1. Answer the following questions. Be sure to show your work. 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 1 1 y=sin 2t += cos 2t where y is the distance from equilibrium (in feet) and t is the time (in seconds). a. Use the identity a.sinB0 + bcos B0 = √a² + b² · sin(Bt + C) where C = arctan (2), a > 0, to write the model in the form y = √a² + b².sin(Bt + C). b. State the amplitude of the oscillations of the weight. c. Find the frequency of the oscillations of the weight.
Transcribed Image Text:1. Answer the following questions. Be sure to show your work. 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 1 1 y=sin 2t += cos 2t where y is the distance from equilibrium (in feet) and t is the time (in seconds). a. Use the identity a.sinB0 + bcos B0 = √a² + b² · sin(Bt + C) where C = arctan (2), a > 0, to write the model in the form y = √a² + b².sin(Bt + C). b. State the amplitude of the oscillations of the weight. c. Find the frequency of the oscillations of the weight.
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