MA2051 - Ordinary Differential Equations
Solutions to Sample Exam 2 - B96

Second Exam - Originally Given 1995 D Term 









1






A


tex2html_wrap_inline39 , z = -x,  tex2html_wrap_inline43 


B


;  tex2html_wrap_inline47 ; M x'' = -Kx - Px'.  With 
    initial conditions, the final model is Mx'' + Px' + Kx = 0, x(0) 
    = 0, x'(0) = 30.


C


The equation is linear and homogeneous.


D


Preventing oscillations requires real characteristic roots: 
     tex2html_wrap_inline57 .  Hence, no oscillations if  tex2html_wrap_inline59 ; the 
    spring can not be too strong lest the system oscillate.


E


Solve Mx'' + Kx = 0, x(0) = 0, x'(0) = 30 to find  tex2html_wrap_inline67 .  Maximum displacement (or 
    amplitude) of  tex2html_wrap_inline69  occurs with  tex2html_wrap_inline71  N/m.










2






A


Via characteristic equation:  tex2html_wrap_inline73 


B


Combine previous homogeneous solution with undetermined 
    coefficients using  tex2html_wrap_inline75 :  tex2html_wrap_inline77 


C


Via characteristic equation:  tex2html_wrap_inline79 


D


Combine previous homogeneous solution with undetermined 
    coefficients using :  tex2html_wrap_inline83 


E


section 8.2, exercise 7








  

    

© 1996 by Will Brother.
All rights Reserved. File last modified on December 6, 1996.