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A 10 kg object is attached to a spring and will stretch the spring 49 cm by itself. A forcing function of the form F(t) = 12 cos(wt) is attached to the object and the system experiences resonance. The object is initially displaced 7.5 cm downward from its equilibrium position and given a velocity of 9 cm/sec upward. Assume there is no damping in the system and displacement and velocity are positive downward. Use g = 9.8 m / s². Keep the coefficients in your answer exact or round them off to at least five decimal places. a) What is the differential equation of the motion? y'' = y' + Y = b) Solve the differential equation to find the displacement as a function of time (t). y(t)

A 10 kg object is attached to a spring and will stretch the spring 49 cm by itself. A forcing function of the form F(t) = 12 cos(wt) is attached to the object and the system experiences resonance. The object is initially displaced 7.5 cm downward from its equilibrium position and given a velocity of 9 cm/sec upward. Assume there is no damping in the system and displacement and velocity are positive downward. Use g = 9.8 m / s². Keep the coefficients in your answer exact or round them off to at least five decimal places. a) What is the differential equation of the motion? y'' = y' + Y = b) Solve the differential equation to find the displacement as a function of time (t). y(t)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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A 10 kg object is attached to a spring and will stretch the spring 49 cm by itself. A forcing function of the form F(t) = 12 cos(wt) is attached to the object and the system experiences resonance. The object is initially displaced 7.5 cm downward from its equilibrium position and given a velocity of 9 cm/sec upward. Assume there is no damping in the system and displacement and velocity are positive downward. Use g = 9.8 m/s². Keep the coefficients in your answer exact or round them off to at least five decimal places. a) What is the differential equation of the motion? y'' + = y' + Y b) Solve the differential equation to find the displacement as a function of time (t). y(t)
Transcribed Image Text:A 10 kg object is attached to a spring and will stretch the spring 49 cm by itself. A forcing function of the form F(t) = 12 cos(wt) is attached to the object and the system experiences resonance. The object is initially displaced 7.5 cm downward from its equilibrium position and given a velocity of 9 cm/sec upward. Assume there is no damping in the system and displacement and velocity are positive downward. Use g = 9.8 m/s². Keep the coefficients in your answer exact or round them off to at least five decimal places. a) What is the differential equation of the motion? y'' + = y' + Y b) Solve the differential equation to find the displacement as a function of time (t). y(t)
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