The motion of a mass-spring system with damping is governed by y''(t) +10y'(t) + ky(t) = 0; y(0)=3, and y'(0) = 0. Find the equation of motion and sketch its graph for k=19, 25, and 31. What is the equation of motion for k=19? y(t) = (Type an exact answer, using radicals as needed.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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The motion of a mass-spring system with damping is governed by the differential equation:

\[ y''(t) + 10y'(t) + ky(t) = 0; \]

with initial conditions:

\[ y(0) = 3, \]
\[ y'(0) = 0. \]

Find the equation of motion and sketch its graph for \( k = 19, 25, \) and \( 31 \).

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**Question:**

What is the equation of motion for \( k = 19 \)?

\[ y(t) = \]

(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: \[ y''(t) + 10y'(t) + ky(t) = 0; \] with initial conditions: \[ y(0) = 3, \] \[ y'(0) = 0. \] Find the equation of motion and sketch its graph for \( k = 19, 25, \) and \( 31 \). --- **Question:** What is the equation of motion for \( k = 19 \)? \[ y(t) = \] (Type an exact answer, using radicals as needed.)
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