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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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' +
b) Solve the differential equation to find the displacement as a function of time (t).
y(t)
Y
Question Help: Message instructor
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Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
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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