- #1

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## 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.