That the displacements u 1 and u 2 of the masses from their equilibrium positions satisfy the equations, u 1 ′ ′ + 5 u 1 = 2 u 2 , u 2 ′ ′ + 2 u 2 = 2 u 1 .

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Answer 1

Question

Chapter 4.2, Problem 29P

(a)

To determine

To show: That the displacements u1 and u2 of the masses from their equilibrium positions satisfy the equations, u1′′+5u1=2u2,u2′′+2u2=2u1.

(b)

To determine

The general solution of the equation, u1(4)+7u1′′+6u1=0.

(c)

To determine

The values of u1′′(0) and u1′′′(0) using u1′′+5u1=2u2,u2′′+2u2=2u1 and the initial conditions u1(0)=1,u1′(0)=0,u2(0)=2,u2′(0)=0 and to show that the solution of u1(4)+7u1′′+6u1=0 satisfies all the four initial conditions given for u1=cost and to show that the corresponding second solution is u2=2cost.

(d)

To determine

The values of u1′′(0) and u1′′′(0) using u1′′+5u1=2u2,u2′′+2u2=2u1 and the initial conditions u1(0)=−2,u1′(0)=0,u2(0)=1,u2′(0)=0 and to show that the solution of u1(4)+7u1′′+6u1=0 satisfies all the four initial conditions given for u1=−2cos6t and to show that the corresponding second solution is u2=cos6t.

(e)

To determine

To describe: The two distinct nodes of vibration from the sub part (c) and (d).

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Answer 2

Question

Chapter 4.2, Problem 29P

(a)

To determine

To show: That the displacements u1 and u2 of the masses from their equilibrium positions satisfy the equations, u1′′+5u1=2u2,u2′′+2u2=2u1.

(b)

To determine

The general solution of the equation, u1(4)+7u1′′+6u1=0.

(c)

To determine

The values of u1′′(0) and u1′′′(0) using u1′′+5u1=2u2,u2′′+2u2=2u1 and the initial conditions u1(0)=1,u1′(0)=0,u2(0)=2,u2′(0)=0 and to show that the solution of u1(4)+7u1′′+6u1=0 satisfies all the four initial conditions given for u1=cost and to show that the corresponding second solution is u2=2cost.

(d)

To determine

The values of u1′′(0) and u1′′′(0) using u1′′+5u1=2u2,u2′′+2u2=2u1 and the initial conditions u1(0)=−2,u1′(0)=0,u2(0)=1,u2′(0)=0 and to show that the solution of u1(4)+7u1′′+6u1=0 satisfies all the four initial conditions given for u1=−2cos6t and to show that the corresponding second solution is u2=cos6t.

(e)

To determine

To describe: The two distinct nodes of vibration from the sub part (c) and (d).

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Answer 3

Question

Chapter 4.2, Problem 29P

(a)

To determine

To show: That the displacements u1 and u2 of the masses from their equilibrium positions satisfy the equations, u1′′+5u1=2u2,u2′′+2u2=2u1.

(b)

To determine

The general solution of the equation, u1(4)+7u1′′+6u1=0.

(c)

To determine

The values of u1′′(0) and u1′′′(0) using u1′′+5u1=2u2,u2′′+2u2=2u1 and the initial conditions u1(0)=1,u1′(0)=0,u2(0)=2,u2′(0)=0 and to show that the solution of u1(4)+7u1′′+6u1=0 satisfies all the four initial conditions given for u1=cost and to show that the corresponding second solution is u2=2cost.

(d)

To determine

The values of u1′′(0) and u1′′′(0) using u1′′+5u1=2u2,u2′′+2u2=2u1 and the initial conditions u1(0)=−2,u1′(0)=0,u2(0)=1,u2′(0)=0 and to show that the solution of u1(4)+7u1′′+6u1=0 satisfies all the four initial conditions given for u1=−2cos6t and to show that the corresponding second solution is u2=cos6t.

(e)

To determine

To describe: The two distinct nodes of vibration from the sub part (c) and (d).

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Answer 4

Question

Chapter 4.2, Problem 29P

(a)

To determine

To show: That the displacements u1 and u2 of the masses from their equilibrium positions satisfy the equations, u1′′+5u1=2u2,u2′′+2u2=2u1.

(b)

To determine

The general solution of the equation, u1(4)+7u1′′+6u1=0.

(c)

To determine

The values of u1′′(0) and u1′′′(0) using u1′′+5u1=2u2,u2′′+2u2=2u1 and the initial conditions u1(0)=1,u1′(0)=0,u2(0)=2,u2′(0)=0 and to show that the solution of u1(4)+7u1′′+6u1=0 satisfies all the four initial conditions given for u1=cost and to show that the corresponding second solution is u2=2cost.

(d)

To determine

The values of u1′′(0) and u1′′′(0) using u1′′+5u1=2u2,u2′′+2u2=2u1 and the initial conditions u1(0)=−2,u1′(0)=0,u2(0)=1,u2′(0)=0 and to show that the solution of u1(4)+7u1′′+6u1=0 satisfies all the four initial conditions given for u1=−2cos6t and to show that the corresponding second solution is u2=cos6t.

(e)

To determine

To describe: The two distinct nodes of vibration from the sub part (c) and (d).

Expert Solution & Answer

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Answer 5

Chapter 4.2, Problem 29P

(a)

To determine

To show: That the displacements u1 and u2 of the masses from their equilibrium positions satisfy the equations, u1′′+5u1=2u2,u2′′+2u2=2u1.

(b)

To determine

The general solution of the equation, u1(4)+7u1′′+6u1=0.

(c)

To determine

The values of u1′′(0) and u1′′′(0) using u1′′+5u1=2u2,u2′′+2u2=2u1 and the initial conditions u1(0)=1,u1′(0)=0,u2(0)=2,u2′(0)=0 and to show that the solution of u1(4)+7u1′′+6u1=0 satisfies all the four initial conditions given for u1=cost and to show that the corresponding second solution is u2=2cost.

(d)

To determine

The values of u1′′(0) and u1′′′(0) using u1′′+5u1=2u2,u2′′+2u2=2u1 and the initial conditions u1(0)=−2,u1′(0)=0,u2(0)=1,u2′(0)=0 and to show that the solution of u1(4)+7u1′′+6u1=0 satisfies all the four initial conditions given for u1=−2cos6t and to show that the corresponding second solution is u2=cos6t.

(e)

To determine

To describe: The two distinct nodes of vibration from the sub part (c) and (d).

Answer 6

Chapter 4.2, Problem 29P

(a)

To determine

To show: That the displacements u1 and u2 of the masses from their equilibrium positions satisfy the equations, u1′′+5u1=2u2,u2′′+2u2=2u1.

Answer 7

Chapter 4.2, Problem 29P

(a)

To determine

To show: That the displacements u1 and u2 of the masses from their equilibrium positions satisfy the equations, u1′′+5u1=2u2,u2′′+2u2=2u1.

Answer 8

(b)

To determine

The general solution of the equation, u1(4)+7u1′′+6u1=0.

Answer 9

(b)

To determine

The general solution of the equation, u1(4)+7u1′′+6u1=0.

Answer 10

(c)

To determine

The values of u1′′(0) and u1′′′(0) using u1′′+5u1=2u2,u2′′+2u2=2u1 and the initial conditions u1(0)=1,u1′(0)=0,u2(0)=2,u2′(0)=0 and to show that the solution of u1(4)+7u1′′+6u1=0 satisfies all the four initial conditions given for u1=cost and to show that the corresponding second solution is u2=2cost.

Answer 11

(c)

To determine

The values of u1′′(0) and u1′′′(0) using u1′′+5u1=2u2,u2′′+2u2=2u1 and the initial conditions u1(0)=1,u1′(0)=0,u2(0)=2,u2′(0)=0 and to show that the solution of u1(4)+7u1′′+6u1=0 satisfies all the four initial conditions given for u1=cost and to show that the corresponding second solution is u2=2cost.

Answer 12

(d)

To determine

The values of u1′′(0) and u1′′′(0) using u1′′+5u1=2u2,u2′′+2u2=2u1 and the initial conditions u1(0)=−2,u1′(0)=0,u2(0)=1,u2′(0)=0 and to show that the solution of u1(4)+7u1′′+6u1=0 satisfies all the four initial conditions given for u1=−2cos6t and to show that the corresponding second solution is u2=cos6t.

Answer 13

(d)

To determine

The values of u1′′(0) and u1′′′(0) using u1′′+5u1=2u2,u2′′+2u2=2u1 and the initial conditions u1(0)=−2,u1′(0)=0,u2(0)=1,u2′(0)=0 and to show that the solution of u1(4)+7u1′′+6u1=0 satisfies all the four initial conditions given for u1=−2cos6t and to show that the corresponding second solution is u2=cos6t.

Answer 14

(e)

To determine

To describe: The two distinct nodes of vibration from the sub part (c) and (d).

Answer 15

(e)

To determine

To describe: The two distinct nodes of vibration from the sub part (c) and (d).

Answer 16

Expert Solution & Answer

Answer 17

Expert Solution & Answer

Answer 18

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Answer 19

Ch. 4.1 - Prob. 1P Ch. 4.1 - Prob. 2P Ch. 4.1 - Prob. 3P Ch. 4.1 - Prob. 4P Ch. 4.1 - Prob. 5P Ch. 4.1 - Prob. 6P Ch. 4.1 - Prob. 7P Ch. 4.1 - Prob. 8P Ch. 4.1 - Prob. 9P Ch. 4.1 - Prob. 10P

That the displacements u 1 and u 2 of the masses from their equilibrium positions satisfy the equations, u 1 ′ ​ ′ + 5 u 1 = 2 u 2 , u 2 ′ ​ ′ + 2 u 2 = 2 u 1 .

To show: That the displacements u1 and u2 of the masses from their equilibrium positions satisfy the equations, u1′​′+5u1=2u2,u2′​′+2u2=2u1.

The general solution of the equation, u1(4)+7u1′​′+6u1=0.

To describe: The two distinct nodes of vibration from the sub part (c) and (d).

Want to see the full answer?

Chapter 4 Solutions

That the displacements u 1 and u 2 of the masses from their equilibrium positions satisfy the equations, u 1 ′ ′ + 5 u 1 = 2 u 2 , u 2 ′ ′ + 2 u 2 = 2 u 1 .

To show: That the displacements u1 and u2 of the masses from their equilibrium positions satisfy the equations, u1′′+5u1=2u2,u2′′+2u2=2u1.

The general solution of the equation, u1(4)+7u1′′+6u1=0.