Solution Found!
All problems refer to the mass–spring
Chapter 4, Problem 5E(choose chapter or problem)
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