Solution Found!
Answer: A simple pendulum (mass M and length L) is
Chapter 11, Problem 11.28(choose chapter or problem)
A simple pendulum (mass M and length L) is suspended from a cart of mass in that moves freely along a horizontal track. (See Figure 11.18, but imagine the spring removed.) (a) What are the normal frequencies? (b) Find and describe the corresponding normal modes. [See the hint for 11.27].
Questions & Answers
QUESTION:
A simple pendulum (mass M and length L) is suspended from a cart of mass in that moves freely along a horizontal track. (See Figure 11.18, but imagine the spring removed.) (a) What are the normal frequencies? (b) Find and describe the corresponding normal modes. [See the hint for 11.27].
ANSWER:Step 1 of 5
(a)
The state of given physical system can be described by applying the Lagrangian function to system, it is expressed as
L=T-V
Here, T is the kinetic energy of the system and V is the potential energy of the system.
The Lagrangian function of a system having generalized coordinates is 
Then the Lagrange’s equations for this conservative system can be expressed as,
