# Derivation of Vibration equation

Can somebody please tell me what should be present in the free body diagram for this system below. Also please mention the arrow details like which direction each force in the free diagram should be acting in. I really need to understand this concept....

OldEngr63
Gold Member
You need to draw two FBDs, one for the housing and one for the rotor. Give that a shot and get back to us. It does you no good if I simply work the problem for you.

I did the diagrams, are they correct?

No. Remember Newton's Third Law. For each internal force (acting between the two bodies), you should show a force and its reaction, one on each FBD.

No. Remember Newton's Third Law. For each internal force (acting between the two bodies), you should show a force and its reaction, one on each FBD.

I have no idea what you are talking about. Are you talking about normal forces in each diagram acting in opposite direction to the mg? Please draw the additional arrows if that's not it

OldEngr63
Gold Member
In the left-hand FBD, where is the force holding up the rotor?

There are other difficulties as well, but this should get you thinking..

You mean I need to put a centrifugal force on the left hand FBD as well? Okay alright that's fine...Is this the final FBD diagram then? Are there any other forces? Tell me if its correct or needs more forces. thanks

OldEngr63
Gold Member
No, it is not correct. There are additional forces required, and the ones you have are not entirely correct.

How can there be other forces? Could you explain. I think I have included all my forces, gravitational forces, damping force, spring force, centrifugal force. What else force do you want....unless you mean reaction forces below the Blue ground in opposite directions to the spring and damping force? Its not like I am not trying to solve this...if you see I am missing something then can you just tell me.

OldEngr63
Gold Member
You show a force on the rotor of mo*ro*w^2 (I presume that is a force, although there is no arrow head). You show a force (a line without arrow head) on the block with the same label but in a different direction. How can this be?

These diagrams has to be right! There can't be anything wrong with this one now. I got the equation of motion and it makes sense. Tell me if you are still not satisfied....Let me know if you are still seeing problems

as the general equation satisfies

M*x"+c*x'+kx = Fcoswt
where F is the external force acting on the system and F = m0*r*w^2 so now I can just write the general equation of motion of the system as
(M+m0)*x"+c*x'+kx = m0*r*w^2 cos wt

OldEngr63
Gold Member
Looks like a step backward. You show on the rotor a force labelled m0*r*w^2 but the reaction to that force does not show on the FBD for the stator. Why is that?