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? b) Solve the differential equation to find the displacement as a function of time (t). y(t) = y = Question Help: Message instructor
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? b) Solve the differential equation to find the displacement as a function of time (t). y(t) = y = Question Help: Message instructor
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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Step 1: Write the general differential equation of motion for the mass spring system
VIEWStep 2: Write the given information
VIEWStep 3: Determine the required differential equation of motion
VIEWStep 4: Use the Laplace transform to find the solution
VIEWStep 5: Use convolution theorem
VIEWStep 6: Simplify the terms
VIEWStep 7: Determine the required solution for y(t)
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