The solution of the differential equation d u d t = − k [ u − T ( t ) ] where T ( t ) = T 0 + T 1 cos ω t .

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Answer 1

Question

Chapter 2.3, Problem 14P

(a)

To determine

The solution of the differential equation dudt=−k[u−T(t)] where T(t)=T0+T1cosωt.

(b)

To determine

To draw: The graphs of steady part S(t) of the solution and the function T(t) on the same axes. From the graph obtain the amplitude R of the steady part of S(t). Also obtain the time lag τ between the respective maxima of T(t) and S(t).

(c)

To determine

The oscillatory part of S(t) in the form of Rcos[ω(t−τ)].

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Answer 2

Question

Chapter 2.3, Problem 14P

(a)

To determine

The solution of the differential equation dudt=−k[u−T(t)] where T(t)=T0+T1cosωt.

(b)

To determine

To draw: The graphs of steady part S(t) of the solution and the function T(t) on the same axes. From the graph obtain the amplitude R of the steady part of S(t). Also obtain the time lag τ between the respective maxima of T(t) and S(t).

(c)

To determine

The oscillatory part of S(t) in the form of Rcos[ω(t−τ)].

Expert Solution & Answer

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See solution

Answer 3

Question

Chapter 2.3, Problem 14P

(a)

To determine

The solution of the differential equation dudt=−k[u−T(t)] where T(t)=T0+T1cosωt.

(b)

To determine

To draw: The graphs of steady part S(t) of the solution and the function T(t) on the same axes. From the graph obtain the amplitude R of the steady part of S(t). Also obtain the time lag τ between the respective maxima of T(t) and S(t).

(c)

To determine

The oscillatory part of S(t) in the form of Rcos[ω(t−τ)].

Expert Solution & Answer

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See solution

Answer 4

Question

Chapter 2.3, Problem 14P

(a)

To determine

The solution of the differential equation dudt=−k[u−T(t)] where T(t)=T0+T1cosωt.

(b)

To determine

To draw: The graphs of steady part S(t) of the solution and the function T(t) on the same axes. From the graph obtain the amplitude R of the steady part of S(t). Also obtain the time lag τ between the respective maxima of T(t) and S(t).

(c)

To determine

The oscillatory part of S(t) in the form of Rcos[ω(t−τ)].

Expert Solution & Answer

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Answer 5

Chapter 2.3, Problem 14P

(a)

To determine

The solution of the differential equation dudt=−k[u−T(t)] where T(t)=T0+T1cosωt.

(b)

To determine

To draw: The graphs of steady part S(t) of the solution and the function T(t) on the same axes. From the graph obtain the amplitude R of the steady part of S(t). Also obtain the time lag τ between the respective maxima of T(t) and S(t).

(c)

To determine

The oscillatory part of S(t) in the form of Rcos[ω(t−τ)].

Answer 6

Chapter 2.3, Problem 14P

(a)

To determine

The solution of the differential equation dudt=−k[u−T(t)] where T(t)=T0+T1cosωt.

Answer 7

Chapter 2.3, Problem 14P

(a)

To determine

The solution of the differential equation dudt=−k[u−T(t)] where T(t)=T0+T1cosωt.

Answer 8

(b)

To determine

To draw: The graphs of steady part S(t) of the solution and the function T(t) on the same axes. From the graph obtain the amplitude R of the steady part of S(t). Also obtain the time lag τ between the respective maxima of T(t) and S(t).

Answer 9

(b)

To determine

To draw: The graphs of steady part S(t) of the solution and the function T(t) on the same axes. From the graph obtain the amplitude R of the steady part of S(t). Also obtain the time lag τ between the respective maxima of T(t) and S(t).

Answer 10

(c)

To determine

The oscillatory part of S(t) in the form of Rcos[ω(t−τ)].

Answer 11

(c)

To determine

The oscillatory part of S(t) in the form of Rcos[ω(t−τ)].

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 2.1 - Prob. 1P Ch. 2.1 - Prob. 2P Ch. 2.1 - Prob. 3P Ch. 2.1 - Prob. 4P Ch. 2.1 - Prob. 5P Ch. 2.1 - Prob. 6P Ch. 2.1 - Prob. 7P Ch. 2.1 - Prob. 8P Ch. 2.1 - Prob. 9P Ch. 2.1 - Prob. 10P

The solution of the differential equation d u d t = − k [ u − T ( t ) ] where T ( t ) = T 0 + T 1 cos ω t .

The solution of the differential equation dudt=−k[u−T(t)] where T(t)=T0+T1cosωt.

To draw: The graphs of steady part S(t) of the solution and the function T(t) on the same axes. From the graph obtain the amplitude R of the steady part of S(t). Also obtain the time lag τ between the respective maxima of T(t) and S(t).

The oscillatory part of S(t) in the form of Rcos[ω(t−τ)].

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