Linearize and solve the equations of motion derived in Problem 11. State all assumptions necessary for the linearization and explain them physically.

Problem 11:

Consider the problem of the "sliding pendulum" drawn in Figure 6.70, where a mass slides along a frictionless rod which is assumed to be uniform and thin. Use

(a) Newton's second law, and

(b) Lagrange's equation to derive the equations of motion. Can the governing equations be linearized? Under what conditions? What happens when \(r=l\) ?

Transcribed Image Text:

M m Figure 6.70: Sliding pendulum.