1.685512.0345118.377J Nonlinear Dynamics and Waves
TakeHome Exam
Thursday, April 5 ,2007
This is a closedbook exum. You may use your own class notes, problem sets and solutions
posted on the 1.685/2.034/18.377 website only. You are not allowed to discus
1.685J/2.0345/18.377J Nonlinear Dynamics and Waves
Spring 2007
Problem Set No. 5
Out: Thursday, April 2 6, 2007
Due: Thursday, May 10, 2007 i n class
Consider a n infinite uniform beam of crosssectional area A , mass per u nit length p , a nd
flexural ri
1.685J/2.0345/18.377J Nonlinear Dynamics and Waves
Spring 2 007
Problem Set No. 4
Out: Thursday, April 1 2, 2007
Due: Thursday, April 2 6, 2 007 i n c lass
Problem 1
Consider t he system
a nd

~ ( x ,t ) = 0 , u ( x , 1 , t ) = 1 for  oo
0
a nd show t h
1.685J/2.0345/18.377J Nonlinear Dynamics and Waves
Spring 2007
Problem Set No. 3
Out: Thursday, March 15, 2007
Due: Thursday, April 5, 2007 i n class
Problem 1
Consider t he Van der Pol oscillator
As discussed in class, t his nonlinear vibratory system ha
1.685J/2.0345/18.377J Nonlinear Dynamics and Waves
Spring 2007
Problem Set N o. 2
O ut: Thursday, March 1, 2007
Due: Thursday, March 15, 2007 i n class
Problem 1
T he cylinder rolls back a nd f orth without slip a s shown i n t he figure below.
( a) Show
1.685J/2.0345/18.377J Nonlinear Dynamics and Waves
Spring 2007
Problem Set No. 1
Out: Thursday, February 15, 2007
Due: Thursday, March 1, 2007 i n class
Problem 1
A m an rows a b oat across a river of width a occupying t he region 0 5 x 5 a in t he x , yp