Explanation Given: The motion of a pair of identical pendulums coupled by a spring is modeled by the system are, m x 1 ′′ = − m g l x 1 − k x 1 + k x 2 m x 2 ′′ = − m g l x 2 − k x 1 + k x 2 Approach: The general solution for the system of equations is solved with the help of Elimination method. The steps are as follows: Step 1 The system is written in operator form; that is, in D , where D = d / d t . Step 2 Eliminate one of the variables, say, y , and solve the resulting equation for x ( t ) .If the system is degenerate then stop. A separate analysis is required to determine whether or not there are solutions. Step 3 If possible, use the system to derive an equation that involves y ( t ) but not its derivatives. Substitute the found expression for x ( t ) into this equation to get a formula for y ( t ) . Step 4 The expressions for x ( t ) and y ( t ) gives the desired solution. Calculation: The given system of equations is given as, ( m D 2 + ( k + m g l ) ) x 1 − k x 2 = 0 ... ( 1 ) ( m D 2 + ( k + m g l ) ) x 2 − k x 1 = 0 ... ( 2 ) Here, D = d d t . Solve the equation ( 1 ) and equation ( 2 ) as follows. Multiply equation ( 1 ) by ( m D 2 + k + m g l ) as, ( m D 2 + k + m g l ) 2 x 1 − k ( m D 2 + k + m g l ) x 2 = 0 … ( 3 ) Multiply equation ( 2 ) by k as k ( m D 2 + ( k + m g l ) ) x 2 − k 2 x 1 = 0 ( 4 ) Add equations ( 3 ) and ( 4 ) as,

Pearson eText Fundamentals of Differential Equations with Boundary Value Problems -- Instant Access (Pearson+)

7th Edition

ISBN: 9780137394524

Author: R. Nagle, Edward Saff

Publisher: PEARSON+

See similar textbooks

Question

Chapter 5.6, Problem 9E

To determine

To find:

The two normal frequencies for the system.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 5.6, Problem 8E

Chapter 5.6, Problem 10E

Students have asked these similar questions

T 1 7. Fill in the blanks to write the calculus problem that would result in the following integral (do not evaluate the interval). Draw a graph representing the problem. So π/2 2 2πxcosx dx Find the volume of the solid obtained when the region under the curve on the interval is rotated about the axis.

38,189 5. Draw a detailed graph to and set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the curve: y = cos²x_for_ |x| ≤ and the curve y y = about the line x = =플 2 80 F3 a FEB 9 2 7 0 MacBook Air 3 2 stv DG

Find f(x) and g(x) such that h(x) = (fog)(x) and g(x) = 3 - 5x. h(x) = (3 –5x)3 – 7(3 −5x)2 + 3(3 −5x) – 1 - - - f(x) = ☐

Chapter 5 Solutions

Pearson eText Fundamentals of Differential Equations with Boundary Value Problems -- Instant Access (Pearson+)

Knowledge Booster

The two normal frequencies for the system.

Solution Summary: The author explains how the system of equations is solved with the help of Elimination method.

To find: The two normal frequencies for the system.

Want to see the full answer?

Chapter 5 Solutions

To find:

The two normal frequencies for the system.