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)
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' +
Y
b) Solve the differential equation to find the displacement as a function of time (t).
y(t)
Expert Solution
Step 1: Introduction of the given problem
We have to model the differential equation and then find its general solution
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