MASSACHUSETTS INSTITUTE OF TECHNOLOGY

DEPARTMENT OF OCEAN ENGINEERING

DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING

13.013J/1.053J Dynamics and Vibration

Fall 2001

Problem Set 7

Assigned: Oct 17, 2001

Due: Oct 24, 11am , 2001

(a) Problem 5.27

(b) Problem 5.31

(c) Problem 5.39

(d) Problem 5.40

(e) Problem 5.41

For deriving the equations of motion, please use both the direct and the variational method and compare the results. From the nonlinear equations of motion, derive the linearized equations of motion. In addition, perform a linear stability analysis for small motion around each static equilibrium position derived from these equations.