How can I solve a dynamic vibration problem?

[deuel18]

Hello. I need some help for my HW. I've been trying this particular problem but I don't know if I am on the right track. The problem and my progress in answering the problem is down below.

 

[Dr.D]

I cannot read your work (I'm an old man with poor eyesight), but this is not a hard problem. Simply write the equation of motion and pull out the effective inertia and the effective stiffness from there.

 

[deuel18]

I cannot read your work (I'm an old man with poor eyesight), but this is not a hard problem. Simply write the equation of motion and pull out the effective inertia and the effective stiffness from there.

I see. I guess my specific question is, if the bar as shown in number 7 is placed as is, should i take into account the weight? Like a suspended mass with spring, the weight is not considered. Is the same applies for this particular problem?

 

[Dr.D]

For your own learning, you should definitely take the weight into account. The implication seems to be that the bar is in equilibrium in the horizontal position shown, so that means that the weight is supported on compression in the spring. Determine the amount of preload on the spring, and then take that and the weight of the bar into account. If done properly, the prelaod and the weight terms should all cancel, leaving you with an equation for small displacements away from equilibrium.

 

[deuel18]

For your own learning, you should definitely take the weight into account. The implication seems to be that the bar is in equilibrium in the horizontal position shown, so that means that the weight is supported on compression in the spring. Determine the amount of preload on the spring, and then take that and the weight of the bar into account. If done properly, the prelaod and the weight terms should all cancel, leaving you with an equation for small displacements away from equilibrium.

I got those in mind but if I choose sum of the moment method at pivot A, it gives mg(L/2) - k(delta)(L) - k(y)(L) = I(alpha). Does that mean mg(L/2) is equal to k(delta)(L)?

 

[Dr.D]

Well, what is the condition for equilibrium?

 

[deuel18]

Ah i see. So the equilibrium cancels the mg with the kdelta.

 

[Dr.D]

Sounds like you've got it.

 

[deuel18]

I do. I was able to do it on other problems. I am just having hard time crunching the numbers right. So i looked for guidance.