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ME 5550 Intermediate Dynamics

Homework #10

1) Find the equilibrium positions of the system of Homework #8,

problem #1, given the following data.

0

4 lb

3 lb

20 lb

p

mg

m g

F

2 ft

17.68 lb/ftk

2) Show that 0x is an equilibrium position for the

system of Homework #8, problem #2. Linearize the

equations of motion about this position and calculate the

natural frequencies and mode shapes of the system using

the following physical data. Describe the motion of each

mode.

1

2

10 lb

5 lb

m g

m g

2 ft

300 lb/ftk

3) Given that 0M and constant , find the

equilibrium positions for the angle for the bar of

Homework #8, problem #3. Then linearize the equation

of motion about these positions. Determine the stability

of small motions about each of these positions. Find the

torque M required so that constant .

4) Given that 0M , constant , and b = 0, show

that the equilibrium position for the angle for the bar

of Homework #8, problem #4 is approximately

58.7 (deg)eq . Then linearize the equation of motion

about this position and determine the stability of small

motions about that position. Find the torque M

required so that constant . Use the following

physical data:

5 lb

2 ft

0

mg

c

10 ft-lb/rad

4 rad/s

k