To prove: The solution of m u ″ + γ u ′ + k u = 0 , u ( 0 ) = u 0 , u ′ ( 0 ) = v 0 is approaches 0 as the value of t approaches ∞ if v 0 = 0 and the system is critically damped. In addition to find the condition on v 0 such that the mass passes through its equilibrium position after it is released if u 0 is positive.

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Answer 1

Question

Chapter 3.7, Problem 14P

To determine

To prove: The solution of mu″+γu′+ku=0, u(0)=u0, u′(0)=v0 is approaches 0 as the value of t approaches ∞ if v0=0 and the system is critically damped. In addition to find the condition on v0 such that the mass passes through its equilibrium position after it is released if u0 is positive.

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Answer 2

Question

Chapter 3.7, Problem 14P

To determine

To prove: The solution of mu″+γu′+ku=0, u(0)=u0, u′(0)=v0 is approaches 0 as the value of t approaches ∞ if v0=0 and the system is critically damped. In addition to find the condition on v0 such that the mass passes through its equilibrium position after it is released if u0 is positive.

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Answer 3

Question

Chapter 3.7, Problem 14P

To determine

To prove: The solution of mu″+γu′+ku=0, u(0)=u0, u′(0)=v0 is approaches 0 as the value of t approaches ∞ if v0=0 and the system is critically damped. In addition to find the condition on v0 such that the mass passes through its equilibrium position after it is released if u0 is positive.

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Answer 4

Question

Chapter 3.7, Problem 14P

To determine

To prove: The solution of mu″+γu′+ku=0, u(0)=u0, u′(0)=v0 is approaches 0 as the value of t approaches ∞ if v0=0 and the system is critically damped. In addition to find the condition on v0 such that the mass passes through its equilibrium position after it is released if u0 is positive.

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Answer 5

Chapter 3.7, Problem 14P

To determine

To prove: The solution of mu″+γu′+ku=0, u(0)=u0, u′(0)=v0 is approaches 0 as the value of t approaches ∞ if v0=0 and the system is critically damped. In addition to find the condition on v0 such that the mass passes through its equilibrium position after it is released if u0 is positive.

Answer 6

Chapter 3.7, Problem 14P

To determine

To prove: The solution of mu″+γu′+ku=0, u(0)=u0, u′(0)=v0 is approaches 0 as the value of t approaches ∞ if v0=0 and the system is critically damped. In addition to find the condition on v0 such that the mass passes through its equilibrium position after it is released if u0 is positive.

Answer 7

Chapter 3.7, Problem 14P

To determine

To prove: The solution of mu″+γu′+ku=0, u(0)=u0, u′(0)=v0 is approaches 0 as the value of t approaches ∞ if v0=0 and the system is critically damped. In addition to find the condition on v0 such that the mass passes through its equilibrium position after it is released if u0 is positive.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 3.1 - Prob. 1P Ch. 3.1 - Prob. 2P Ch. 3.1 - Prob. 3P Ch. 3.1 - Prob. 4P Ch. 3.1 - Prob. 5P Ch. 3.1 - Prob. 6P Ch. 3.1 - Prob. 7P Ch. 3.1 - Prob. 8P Ch. 3.1 - Prob. 9P Ch. 3.1 - Prob. 10P

To prove: The solution of mu″+γu′+ku=0, u(0)=u0, u′(0)=v0 is approaches 0 as the value of t approaches ∞ if v0=0 and the system is critically damped. In addition to find the condition on v0 such that the mass passes through its equilibrium position after it is released if u0 is positive.

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Chapter 3 Solutions