All problems refer to the mass–spring

Chapter 4, Problem 5E

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QUESTION:

The motion of a mass-spring system with damping is governed by

     \(y^{\prime \prime}(t)+10 y^{\prime}(t)+k y(t)=0\) ;

     \(y(0)=1\) ,     \(y^{\prime}(0)=0\) .

Find the equation of motion and sketch its graph for \(k=20\), 25, and 30.

Equation Transcription:

Text Transcription:

y"(t)+10y'(t)+ky(t)=0

y(0)=1

y'(0)=0

k=20

Questions & Answers

QUESTION:

The motion of a mass-spring system with damping is governed by

     \(y^{\prime \prime}(t)+10 y^{\prime}(t)+k y(t)=0\) ;

     \(y(0)=1\) ,     \(y^{\prime}(0)=0\) .

Find the equation of motion and sketch its graph for \(k=20\), 25, and 30.

Equation Transcription:

Text Transcription:

y"(t)+10y'(t)+ky(t)=0

y(0)=1

y'(0)=0

k=20

ANSWER:

SOLUTION

Step 1

In this problem, we are asked to find the equation of motion and sketch its graph for .

Initial conditions are

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