# Mechanical Vibration: 3 Degree of Freedom

## Homework Statement

http://i.imgur.com/wJu0AEs.jpg
http://i.imgur.com/J9sEWgq.jpg?1

## Homework Equations

Kinetic Energy = T = 1/2 * I * (theta_dot)^2
Potential Energy = V = 1/2 * Kt * theta^2

## The Attempt at a Solution

Matlab Code and Results:
>> I1=3600;
I2=200;
I3=800;
I4=4800;
d1=0.15;
L1=3.5;
d2=0.2;
L2=3;
G=80e9;
J1=(pi/32) *d1^4
J2=(pi/32) *d2^4
Kt1= (J1*G)/L1
Kt2 =(J2*G)/L2
II = [I1 0 0;0 I2+I3 0;0 0 I4]
KK=[Kt1 -Kt1 0;-Kt1 Kt1+Kt2 -Kt2;0 -Kt2 Kt2]

J1 =

4.9701e-05

J2 =

1.5708e-04

Kt1 =

1.1360e+06

Kt2 =

4.1888e+06

II =

3600 0 0
0 1000 0
0 0 4800

KK =

1.0e+06 *

1.1360 -1.1360 0
-1.1360 5.3248 -4.1888
0 -4.1888 4.1888

>> AA = inv(II)*KK

AA =

1.0e+03 *

0.3156 -0.3156 0
-1.1360 5.3248 -4.1888
0 -0.8727 0.8727

>> [V,D] = eig(AA)

V =

0.0538 0.7956 0.5774
-0.9849 -0.2764 0.5774
0.1648 -0.5391 0.5774

D =

1.0e+03 *

6.0878 0 0
0 0.4252 0
0 0 0.0000

The problem is that I am getting lmbda1=0 which means the first fundamental frequency is zero ... and it is mentioned in the second part of the problem that f2=3.89 Hz and In my solution it does not equal that.
Can you please go through my steps and tell me what is wrong.