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The motion of a mass-spring system with damping is governed by y''(t) + by' (t) + 64y(t) = 0; y(0) = 5, and y'(0) = 0. Find the equation of motion and sketch its graph for b=0, 12, 16, and 20. What is the equation of motion for b=0? y(t) = (Type an exact answer, using radicals as needed.)

The motion of a mass-spring system with damping is governed by y''(t) + by' (t) + 64y(t) = 0; y(0) = 5, and y'(0) = 0. Find the equation of motion and sketch its graph for b=0, 12, 16, and 20. What is the equation of motion for b=0? y(t) = (Type an exact answer, using radicals as needed.)

Advanced Engineering Mathematics
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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The motion of a mass-spring system with damping is governed by the differential equation: \[ y''(t) + by'(t) + 64y(t) = 0 \] with initial conditions \( y(0) = 5 \) and \( y'(0) = 0 \). Find the equation of motion and sketch its graph for \( b = 0, 12, 16, \) and \( 20 \). --- **Task:** What is the equation of motion for \( b = 0 \)? \[ y(t) = \] (Type an exact answer, using radicals as needed.)
Transcribed Image Text:The motion of a mass-spring system with damping is governed by the differential equation: \[ y''(t) + by'(t) + 64y(t) = 0 \] with initial conditions \( y(0) = 5 \) and \( y'(0) = 0 \). Find the equation of motion and sketch its graph for \( b = 0, 12, 16, \) and \( 20 \). --- **Task:** What is the equation of motion for \( b = 0 \)? \[ y(t) = \] (Type an exact answer, using radicals as needed.)
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