MA2051  Ordinary Differential Equations
Solutions to Sample Exam 2  B96
Second Exam  Originally Given 1995 D Term

1


A

, z = x,

B

; ; 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:
. Hence, no oscillations if ; the
spring can not be too strong lest the system oscillate.

E

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

2


A

Via characteristic equation:

B

Combine previous homogeneous solution with undetermined
coefficients using :

C

Via characteristic equation:

D

Combine previous homogeneous solution with undetermined
coefficients using :

E

section 8.2, exercise 7
© 1996 by Will Brother.
All rights Reserved. File last modified on December 6, 1996.