That the equation of the trajectories of the undamped pendulum can be written as 1 2 y 2 + ω 2 ( 1 − cos x ) = c .

Question

Want to see the full answer?

Answer 1

Question

Chapter 9.3, Problem 22P

(a)

To determine

To show: That the equation of the trajectories of the undamped pendulum can be written as 12y2+ω2(1−cosx)=c.

(b)

To determine

To prove: The expression 12mL2(dθdt)2+mgL(1−cosθ)=E.

(c)

To determine

To show: The kinetic energy of the pendulum and that the second term is the potential energy due to gravity.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

Question 1. Prove that the function f(x) = 2; f: (2,3] → R, is not uniformly continuous on (2,3].

Consider the cones K = = {(x1, x2, x3) | € R³ : X3 ≥√√√2x² + 3x² M = = {(21,22,23) (x1, x2, x3) Є R³: x3 > + 2 3 Prove that M = K*. Hint: Adapt the proof from the lecture notes for finding the dual of the Lorentz cone. Alternatively, prove the formula (AL)* = (AT)-¹L*, for any cone LC R³ and any 3 × 3 nonsingular matrix A with real entries, where AL = {Ax = R³ : x € L}, and apply it to the 3-dimensional Lorentz cone with an appropriately chosen matrix A.

I am unable to solve part b.

Answer 2

Question

Chapter 9.3, Problem 22P

(a)

To determine

To show: That the equation of the trajectories of the undamped pendulum can be written as 12y2+ω2(1−cosx)=c.

(b)

To determine

To prove: The expression 12mL2(dθdt)2+mgL(1−cosθ)=E.

(c)

To determine

To show: The kinetic energy of the pendulum and that the second term is the potential energy due to gravity.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 9.3, Problem 22P

(a)

To determine

To show: That the equation of the trajectories of the undamped pendulum can be written as 12y2+ω2(1−cosx)=c.

(b)

To determine

To prove: The expression 12mL2(dθdt)2+mgL(1−cosθ)=E.

(c)

To determine

To show: The kinetic energy of the pendulum and that the second term is the potential energy due to gravity.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 9.3, Problem 22P

(a)

To determine

To show: That the equation of the trajectories of the undamped pendulum can be written as 12y2+ω2(1−cosx)=c.

(b)

To determine

To prove: The expression 12mL2(dθdt)2+mgL(1−cosθ)=E.

(c)

To determine

To show: The kinetic energy of the pendulum and that the second term is the potential energy due to gravity.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 9.3, Problem 22P

(a)

To determine

To show: That the equation of the trajectories of the undamped pendulum can be written as 12y2+ω2(1−cosx)=c.

(b)

To determine

To prove: The expression 12mL2(dθdt)2+mgL(1−cosθ)=E.

(c)

To determine

To show: The kinetic energy of the pendulum and that the second term is the potential energy due to gravity.

Answer 6

Chapter 9.3, Problem 22P

(a)

To determine

To show: That the equation of the trajectories of the undamped pendulum can be written as 12y2+ω2(1−cosx)=c.

Answer 7

Chapter 9.3, Problem 22P

(a)

To determine

To show: That the equation of the trajectories of the undamped pendulum can be written as 12y2+ω2(1−cosx)=c.

Answer 8

(b)

To determine

To prove: The expression 12mL2(dθdt)2+mgL(1−cosθ)=E.

Answer 9

(b)

To determine

To prove: The expression 12mL2(dθdt)2+mgL(1−cosθ)=E.

Answer 10

(c)

To determine

To show: The kinetic energy of the pendulum and that the second term is the potential energy due to gravity.

Answer 11

(c)

To determine

To show: The kinetic energy of the pendulum and that the second term is the potential energy due to gravity.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 15

Ch. 9.1 - Prob. 1P Ch. 9.1 - Prob. 2P Ch. 9.1 - Prob. 3P Ch. 9.1 - Prob. 4P Ch. 9.1 - Prob. 5P Ch. 9.1 - Prob. 6P Ch. 9.1 - Prob. 7P Ch. 9.1 - Prob. 8P Ch. 9.1 - Prob. 9P Ch. 9.1 - Prob. 10P

That the equation of the trajectories of the undamped pendulum can be written as 1 2 y 2 + ω 2 ( 1 − cos x ) = c .

Concept explainers

Videos

To show: That the equation of the trajectories of the undamped pendulum can be written as 12y2+ω2(1−cosx)=c.

To prove: The expression 12mL2(dθdt)2+mgL(1−cosθ)=E.

To show: The kinetic energy of the pendulum and that the second term is the potential energy due to gravity.

Want to see the full answer?

Chapter 9 Solutions